SOIL DYNAMICS in TILLAGE and TRACTION

î4% SOIL DYNAMICS in TILLAGE AND TRACTION

Agriculture Handbook No. 316

Agricultural Research Service UNITED STATES DEPARTMENT OF AGRICULTURE

MBP0000263

SOIL DYNAMICS in TILLAGE AND TRACTION

WILLIAM R. GILL Soil Scientist Agricultural Engineering Research Division and Soil and Water Conservation Research Division

GLEN E. VANDEN BERG Agricultural Engineer Agricultural Engineering Research Division

Agricultural Research Service UNITED STATES DEPARTMENT OF AGRICULTURE Trade names are used in this publication solely to provide specific information. Mention of a trade name does not constitute a warranty of the product by the U.S. Department of Agriculture or an endorse- ment of the product to the exclusion of other products not mentioned.

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One of the most difficult problems of research workers, teachers, and application engineers in any scientific and technical effort is to obtain all of the existing pertinent knowledge on the specific subject being investigated, taught, or applied. There are at least two approaches to the solution of this problem. One is to develop facilities for the ready retrieval of any publication pertinent to the specific subject. This approach is receiving wide support, and good progress is being made by research and education institutions, professional societies, and libraries in evolving rather effective though often quite sophisticated systems of retrieving information. A second approach is to review, relate, evaluate, and assemble in one volume or set of volumes all significant facts on a specific subject. This is a tedious, time-consummg activity, which requires broad understanding and great skill. However, if well done, such reviews are of great value to the scientific community. In fact, for the progress of any discipline, periodic reviews of this type are an essential supplement to even the best information retrieval system. They serve as mileposts along the highway of knowledge. SOIL DYNAMICS IN TILLAGE AND TRACTION is such a milepost. EUGENE G. MCKIBBEN, Director Agricultural Engineering Research Division Agricultural Research Service U.S. Department of Agriculture Preface

Soil dynamics is defined as the branch of knowledge that considers the motion of soil. Soil movement results from man's attempts (1) to change prevailing soil conditions to those that are more suitable or (2) to use soil for support and locomotion of vehicles. The scope of soil dynamics thus includes soil-machine relations in both tillage and traction. It is not restricted to agricultural soils and problems since information on basic soil behavior is universally applicable. The tremendous amount of earth construction and land forming throughout the world has made machine handling of soil increasingly important in construction, military, and mining operations. The final applications of soil dynamics knowledge may differ, but the principles are independent of application. This handbook is an attempt to convey both definitive and practical information concerning soil dynamics to persons interested in tillage and traction. The information has been brought together and developed in conjunction with the research program of the National Tillage Machinery Laboratory, Auburn, Ala. This is a handbook of ideas and concepts rather than methods or procedures. The ideas stem from an attempt to w^eld a comprehensive organization of isolated bits of information into a coherent body of knowledge that is designated soil dynamics. An attempt has been made to be analytical as well as descriptive so that the significance of data in the literature can be established. Where possible, mathematical treatment has been developed in quantitative terms to express specific soil-machine relations on the assumption that these relations must obey fundamental laws. Basic forms of soil behavior such as shear failure and sliding friction have been identified and quantitatively described by behavior equations. Principles by which subordinate behaviors can be isolated and quantitatively described are suggested. Definitive parameters are inherent in each basic equation that describes a soil behavior. These parameters, when identified and evaluated, provide a basis for characterizing soil with regard to its movement behavior. The feasibility of combining behavior equations into a simple soil- machine mechanics is demonstrated. The procedure by which a complete mechanics can be developed is described. Such a mechanics is capable of describing and predicting the action of machines in terms of performance. Criteria of performance are proposed and defined. An evaluation of these criteria provides a basis for the design of machines whose actions can be controlled and optimized. Since only rudimentary behavior equations and soil-machine mechanics are available today, a sound theoretical basis for designing soil tillage and traction machines does not exist. In the absence of theoretical approaches, empirically established equations are proposed PREFACE as practical alternates. When properly developed, these equations will provide information for designing soil tillage and traction machines. The information will also contribute to the development of a rigorous theoretical mechanics. No attempt has been made to solve problems; rather it is established that soil dynamics provides a fundamental approach for so doing. This handbook has attempted to develop soil dynamics in depth, scope, and extent so that it defines and delineates an area of knowledge that will be a new discipline. Eesearch goals have been suggested which should provide the information required to solve most problems in soil dynamics. Acknowledgment is made to A. W. Cooper, W. F. McCreery, M. L. Nichols, C. A. Eeaves, and I. F. Eeed, who are members of the National Tillage Machinery Laboratory staff, for assistance during the preparation and review of the handbook. Special acknowledgment is made to E. G. McKibben, W. M. Carleton, L. A. Liljedahl, and S. W. McBirney of the Agricultural Engineering Eesearch Division, Beltsville, Md., for their encourage- ment and support of the project. Acknowledgment is made to technical reviewers who are not members of the National Tillage Machinery Laboratory Staff. They are : W. F. Buchele, Agricultural Engineering Department, Iowa State University ; L. O. Drew and T. H. Garner, Agricultural Engineering Department, Clemson University; J. G. Hendrick, Department of Agricultural Engineering, Auburn University; L. Johnson, Agricul- tural Engineering Department, International Eice Eesearch Insti- tute; S. Persson, Agricultural Engineering Department, Michigan State University; J. A. Weber, Department of Agricultural Engi- neering, University of Illinois; J. L. Dais, D. N. Koppes, N. Osifchm, A. G. Vedejs, G. F. Weissmann, E. N. White and W. W. Wood, members of the technical staff. Bell Telephone Laboratories. Contents

1. INTRODUCTION 1 1.1 Historical 1 1.2 Soil Dynamics 3 1.3 Research Centers 5 1.3.1 The National Tillage Machinery I^aboratory, Auburn, Ala. 6 1.3.2 The Army Mobility Research Center, Vicksburg, Miss. 7 1.3.3 The Land Locomotion Laboratory, Warren, Mich. 8 1.3.4 The National Institute of Agricultural Engineering, Silsoe, England 8 1.3.5 Institute of Fundamental Research in Agricultural Engineering, Volkenrode, Germany 10 1.3.6 Institute for Agricultural Mechanization, Konosu, Japan 11 1.3.7 Other Research Centers 11 2. DYNAMIC PROPERTIES OF SOILS 14 2.1 Introduction 14 2.2 Stress in Soil 14 2.3 Strain in Soil 17 2.4 Stress-Strain Relations __ _ Z_~ZI 20 2.5 Soil Strength '___ 22 2.6 Stress Distribution _~II_ II_ 23 2.7 Strain Distribution _ _ _ _ _~~~___I"_" ..29 2.8 Yield in Soil __ I" __"_'_ __ "_""!""" 31 2.8.1 Shear IIII—II-"_-I_-I__II_I_._"_I 32 2.8.2 Compression __ 36 2.8.3 Tension _ _ _ ~~ ___ 37 2.8.4 Plastic Flow I_ _""" _ 39 2.9 Rigid Body Soil Movement I__I_ZIII_I 39 2.9.1 Momentum ~~ "~ Z"Jl ~ 40 2.9.2 Friction IIIIIIII_IIII__I__ _ 40 2.9.3 Adhesion IIIIIII_I_ZI_"~II_I 42 2.9.4 Abrasion II_I~I~II II __"_ II 52 2.10 Dynamic Versus Static Properties ___I__I_I_ I_ I "_"_" _"_I_ 53 3. ASSESSMENT OF THE DYNAMIC PROPERTIES OF SOIL" "___ 55 3.1 Soil as a Physical System _ _ 55 3.2 Dynamic Parameters I" I I H "I QQ 3.2.1 Measuring Independent Parameters _I __~ _ _ ~~ 65 3.2.1.1 Shear __II I_~II aí 3.2.1.2 Tension IIIIIII Z.Jl.JlJl^ 74 3.2.1.3 Compression ______CA 3.2.1.4 Plastic Flow __"_ öQ 3.2.1.5 Friction I_ 22 3.2.1.6 Adhesion I-I-I'III _"~_'r_~~rri 89 3.2.2 Measuring Composite Parameters QQ 3.2.2.1 Penetration _ _ _ 04 3.2.2.2. Bearing Strength 3.2.2.3 Induced Strength ______100 3.3 Measuring Gross Dynamic Behavior 1X9 3.3.1 Rupture ~""~_ IAQ 3.3.2 Blast Erosion i}t¿ 3.3.3 Abrasion I ,XQ 3.3.4 Movement -"""IIIHIIIIIIIIIIIIIII—I—I 113 VI CONTENTS Vil

4. MECHANICS OF TILLAGE TOOLS 117 4.1 Introduction }}! 4.2 The Reaction of Soil to Tillage Tools li¿ 4.2.1 Principles for Developing a Mechanics ll» 4.2.2 The Complete Soil-Tillage Tool Mechanics 122 4.3 Mechanics of Simple Reactions 125 4.3.1 Inclined Tools 1^^ 4.3.2 Vertical Tools 1^^ 4.3.3 Cutting of Soil 14« 4.3.4 Conclusions l^jj 4.4 Soil Behavior in Simplified Systems l^Y 4.4.1 Soil-Metal Sliding 161 4.4.1.1 Measurement of Sliding Actions loi 4.4.1.2 The Sliding Path 170 4.4.1.3 Mechanics for Draft Force of Sliding Actions 171 4.4.1.4 Scouring ^— 176 4.4.2 Penetration 181 4.5 Geometry of Soil-Tool Systems 191 4.5.1 Alteration of Tool Geometry by the Formation and Adherence of Soil Bodies 192 4.5.2 Alteration of Tool Geometry Because of Wear 194 4.5.3 Soil-Tool Geometry 198 4.5.4 Orientation of the Soil-Tool System 205 4.5.5 Geometry of Interacting Tools 207 4.5.6 Conclusions 208 4.6 Mechanics of Complex Reactions 209 5. DESIGN OF TILLAGE TOOLS 211 5.1 Introduction 211 5.2 The Design Equations 212 5.3 Shape 219 5.3.1 Soil Loosening and Turning Tools 220 5.3.1.1 Macroshape 221 5.3.1.2 Microshape and Friction 232 5.3.1.3 Edgeshape and Wear 242 5.3.2 Soil Transporting Tools 249 5.3.3 Conclusions 255 5.4 Manner of Movement 255 5.4.1 Orientation 256 5.4.2 Path of Motion 260 5.4.3 Speed 263 5.5 Multipowered Tools 265 5.5.1 Electro-osmosis 266 5.5.2 Rotating Tools 269 5.5.3 Oscillating Tools 279 5.6 Implements — 288 5.7 Principles of Force Application 295 6. PERFORMANCE OF TILLAGE TOOLS 298 6.1 Introduction 298 6.2 Description of Soil Conditions 300 6.3 Objectives of Tillage 308 6.4 Measuring Performance 310 6.4.1 Forces 310 6.4.2 Soil Conditions 318 6.4.2.1 Breakup 319 6.4.2.2 Segregation 322 6.4.2.3 Mixing 325 6.4.3 Specialized Tillage Actions 326 6.4.3.1 Handling Plant Residue 326 6.4.3.2 Insertion of Foreign Materials into Soil 330 6.4.3.3 Separating 332 6.5 Evaluating Performance 334 MECHANICS OF TRACTION AND TRANSPORT 340 7.1 Introduction 340 7.2 Mechanics of Traction Devices 341 7.2.1 Nonrolling Traction Devices 342 vin CONTENTS 7.2.2 Rolling Traction Devices 345 7.2.3 Transport Devices 354 7.3 Characterizing Traction and Transport Devices 355 7.3.1 Dynamic Stress Distributions 355 7.3.2 Deflections or Movements Between Devices and the Soil 362 7.3.3 The Shape of the Contact Surface 364 7.4 Evaluating Traction Performance 365 7.4.1 Criteria of Performance 366 7.4.1.1 Drawbar Pull 366 7.4.1.2 Speed and Slip 368 7.4.1.3 Energy Efíiciency 374 7.4.1.4 Load-carrying Capacity 376 7.4.2 Measures of Performance 377 7.4.3 Evaluation of Performance 379 7.5 Design of Traction and Transport Devices 381 7.5.1 Transport Devices 386 7.5.2 Driven Wheels 392 7.5.3 Tracks 405 7.5.4 Auxiliary Devices I 410 7.5.5 Operational Control of Design Factors 413 7.6 Vehicle Design, Use, and Performance 416 7.6.1 Vehicle Morphology 416 7.6.2 Vehicle Capabilities IIIII_II__ 417 7.7 Relative Importance of the Soil and the Vehicle on Traction and Transport Capabilities 419 7.8 Predicting Traction Performance 420 8. SOIL COMPACTION I III"..!!!!! 430 8.1 Introduction ~ " 430 8.2 Compaction Behavior Equations l^l 2__2 I I 431 8.3 Compaction in Tillage and Traction " 441 9. SOIL DYNAMICS IN SOIL-MACHINE SYSTEMS _" 447 9.1 Systems Analysis 447 9.2 Soil Dynamics as a Discipline II " _ 450 9.3 Soil Dynamics and Tillage ~ I ~_I_ _" ~I_ 452 9.4 Soil Dynamics and Traction ___ I~I II__ I I__ AKQ 9.5 Conclusions - - - _ 10. SELECTED REFERENCES _ _ __" TaL 11. GLOSSARY "_"" 1^^ 12. INDEX _I___ 1^^ 1. INTRODUCTION

1.1 Historical Soil dynamics, a phase of soil science and mechanics concerned with soiîs in motion, may be defined as the relation between forces applied to the soil and the resultant soil reaction. This definition does not restrict the source of the force applied to the soil ; consequently, the dynamic reactions that result from the natural forces of wind, water, and other sources are included. Reactions due to wind and water are of paramount importance in erosion and hydrology and the mechanics of these reactions are being studied ( 72, 391 )} Only reactions caused by mechanical forces applied directly to the soil are considered here. The dynamic reactions of soil in tillage and traction affect the design and use of machines that handle soil. Because the interrelations are of primary interest, ihç^ tool (or traction device) and the soil must be considered together. In order not to restrict the final application of the research findings, tillage is defined as mechanical manipulation of the soil (for any purpose). This definition may be difficult to accept, but the same type of plow that plows soil for agricultural purposes may also be the basic tillage unit of a machine that lays antitank mines for military purposes. The bulldozer does exactly the same work when leveling land for irrigation and drainage purposes as when leveling land for new buildings, roads, and parks. Tillage is therefore defined in terms of applying forces rather than in terms of the reason for which the forces are applied. . Traction is the force derived from the soil to pull a load. This torce is exerted against the soil by a traction device such as a wheel, track, winch sprag, or spade. The dynamic resistance of the soil to provide traction is supplied through an interaction between the traction device and the soil. This interaction is very complex and little head- way has been made in solving some of the problems that result from the interaction. The practical importance of soil dynamics in tillage and traction has been known for many years; however, soil dynamics research has been conducted only since 1920. Until that time no concerted effort was made to bring information together and to direct research along fundamental lines so as to solve complex problems in tillage and traction. What may have been the first doctorate thesis in agricultural engineering in the United States was written by E. A. White at Cornell University in 1918. It was entitled "A Study of the Plow Bottom and its Action Upon the Furrow Slice." No doubt this thesis will stand as í\\Q landmark identifying the point where a more theoretical approach in the study of tillage tools began.

1 Italic numbers in parentheses refer to Selected References, p. 460. 1 ^ AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE The initial flourish of research in soil dynamics that was started in the 1920's increased until the mid-1930's, at which time it di- minished for several reasons. Certainly the economic depression in the 1930's and World War II w^ere major contributing factors. In addition, however, agricultural production increased tremendously because of mechanization of agriculture and heavy applications of fertilizer. Eesearch funds were directed toward this type of research. One additional factor, which was by no means of minor importance, was that the personnel who had been active in the original surge of research moved into different positions. Frequently these positions were administrative or were no longer allied with soil dynamics research. Since most of the research was conducted by individual workers, the programs were not self-perpetuating after the worker left his assignment. Advances in soil dynamics research since 1950 indicate that it is again becoming a fully recognized area of research. The American Society of Agricultural Engineers (ASAE) aided greatly in establishing soil dynamics as a distinct and fundamental area of research. The details of this recent activity are well known in comparison to other areas of research. According to Baver {32 )^ Schubler was apparently the first to present a comprehensive and systematic picture of the physical properties of soil. In a similar manner. Baver {32 ) singles out Wollny as the individual who defined the physical properties of soils from the point of view of plant growth. Terzaghi and Peck ( 4^7 ) and others ( 18^^ 4^1 ) unified soil mechanics into a separate entity. The inspiration for each of these studies undoubtedly came from a large number of individuals whose names are not known. Nevertheless, these individuals spun the loose fibers of diverse facts into a thread of organized knowledge. In soil dynamics, undoubtedly the basic research of White ( 502^ 503 ) pointed out the possibilities of research along rigorous lines. Initially, the inspiring force came largely from R. W. Trullinger, who was then in the Office of Experiment Stations, Department of Agriculture. As chairman of the ASAE's Research Committee, he advocated basic research and led the Society into an era of stimulating research in soil dynamics ( 4^8-441 ). However, the systematic, basic research program under the leadership of M. L. Nichols, then of the Alabama Agricultural Experiment Station, should be recognized. Much of the work of Nichols and his colleagues was published in Agricultural Engineering under the title Soil Dynamics, and the series of articles proved to be a classical series of papers for that journal ( 105,106, 234, 235, 312-320 ). This work and other work in the field at Prattville, Ala., led to the establishment of the National Tillage Machinery Laboratory. Plans and suggestions of the personnel of the Alabama Polytechnic Institute (now Auburn University) and the Bureau of Agricultural Engineering (now a part of the Agricultural Research Service) of the U.S. Department of Agricul- ture were developed into a proposal. Supported by the American Farm Bureau Federation, the proposal ultimately resulted in legisla- tion that established the Laboratory as a USD A facility at Auburn, Ala., in 1935. Simultaneously with the development of soil dynamics in the United States, research in the same general area was being con- SOIL DYNAMICS IN TILLAGE AND TRACTION ó ducted at the Kothamsted Experiment Station, England. The imagi- nation, versatility, and productivity of the research of this Station was outstanding and has been reviewed in considerable detail by Keen ( 214 ) ; most of the reports on this research were published in the Journal of Agricultural Science. Similarly, Russian and German scientists have been extremely productive in soil dynamics research ( 28^ 103^ 158^ 3^2^ 515 ). Not all soil dynamics research, however, was conducted in conjunction with agriculture. C. F. Jenkin, a British civil engineer, suggested in 1932 that the experimental work of Eathje and the theoretical work of Love provided a basis for urgently needed research on plowing ( 201 ). 1.2 Soil Dynamics A collective undertaking of the ASAE research committee resulted in a comprehensive review by McKibben ( 266 ) of the factors involved in soil dynamics. A brief summary of that report follows: 1. Natural soil is a result of geology, climate, and vegetation and the time that the last two agents have been acting on the first. 2. Soils are modified by amendments, weather, and tillage and other management practices. 3. A soil thus formed can be described by the condition of the following physical, biological, and chemical properties: a. Weathered solid matter: Elements, inorganic compounds, organic compounds, organisms, texture, shape of particles, and structure, size, shape, and arrangement of the aggregates. b. Un weathered solid matter : Eocks and gravel ; plant material. c. Liquid: Solvent and solute. d. Temperature of soil. 4. Certain composite properties made up of a number of physical, chemical, and biological properties listed in item 3 have been used in attempts to make comparisons. These include moisture coefficients, specific gravity, and volume weight. 5. A definite atomic and molecular attraction complex results from any combination and arrangement of the chemical, physiological, and biological properties. This complex produces a definition of these properties described as— a. Cohesion (attraction between like molecules). b. Adhesion (attraction between unlike molecules). 6. Certain working or shaping characteristics of a soil are caused by the complexes mentioned in item 5. a. Degree of plasticity (relation of elastic limit and point of rupture). b. Degree of hardness (relative resistance to permanent deformation). c. In most materials these characteristics are determined by empirical methods and expressed by arbitrary scales. 7. Certam relatively simple mechanical properties are also caused by the complexes mentioned in item 5. a. Tensile strength (tenacity). b. Compressive strength. c. Shearing strength. d. Friction coefficients. e. Modulus of elasticity. 4 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE These mechanical properties may be determined by more or less standardized tests based on mathematical principles. 8. Certain composite mechanical properties are also caused by the complex factors mentioned in item 5. a. Resistance to penetration. b. Bearing strength. c. Tillage resistance characteristics. d. Traction characteristics. Tests for these properties have been and probably will continue to be empirical in nature. Evaluation of soil is still largely based on the concepts embodied in the report by McKibben. Whiíe we have made some advances in areas not specifically included in the foregoing outline, these advances have merely expanded some of the major outlined points. Nichols ( 3H ) formulated and organized the elements of soil d^^namics and provided a general classification of the variables in soil dynamics studies. He posed questions that needed to be answered by work in soil dynamics. These qnestion&Tiot only established the scope of the problem but also served as a basis on which to establish research objectives. The following types of questions were used: What design of plow bottom is best adapted for push-soils ? What design of plow will accomplish a given objective with the least draft? What size of wheel and width of tire are most desirable for a given load on a given soil? Having established the scope of the soil dynamics problem, Nichols pointed to two research ob]ectives: (1) to determine the reaction properties of the soil to applied force as a basis for designing implements; and (2) to design simple tests by which soils can be compared or their actions can be accurately predetermined. Inherent in attaining the first objective is a logical method of procedure, which is to determine the soil and implement variables that enter into tillage problems and the interrelation of these variables. Nichols suggested a classification of the variables entering into soil dynamics studies for use in obtaining the second objective. 1. Primary soil factors (measurable or controllable) : particle size, colloidal content, moisture (percentage), apparent specific gravity (state of compaction), organic matter, chemical composition of colloid. 2. Design variables (controllable) : kind of metal, polish, bearing area, curvature of surface applying force. 3. Dynamic properties of the soil (measurable) : coefficient of internal resistance (or shear value), friction, resistance to compression, adhesion, moment of inertia. 4. Dynamic resultants (measurable) : fragmentation, arch action, compaction, shear. The interrelations among these factors constitute cause-and-efïect relationships. Indeed, the accurate prediction of the reaction of a soil to a force, as sought by Nichols, is more nearly the purpose of a soil-machine mechanics than is a classification scheme. Given all of the parameters and relations that describe a reaction, the elements may then be classified into certain general natural relationships. The major emphasis in this handbook is to examine the information that is available or that is needed to establish accurate relationships. SOIL DYNAMICS IN TILLAGE AND TRACTION Ö The inability to measure and characterize soils has been the limiting factor in soil dynamics. The factors suggested by Nichols may presumably be related to each other in some quantitative fashion. Soil dynamics constitutes the basis on which to establish, interpret, and use all of the possible relations that are involved. The problem may be broken down into two general areas that center around practical objectives: (1) a basic area, in which soil-machine dynamic relations and interactions are established; (2) an application area, in which the performance of a machine in a soil system is determined. The soil-machine mechanics should apply to all possible soil reactions and serve as a basis on which the dynamic properties of soil can be used. Evalua- tion of performance cannot be restricted to dynamic properties since economic, soil, machine, plant, social, and other factors must be considered. The number and kind of factors to be considered depend on the specific application. 1.3 Research Centers Following the decline in research in soil dynamics during World War II, the resumption of research was slow. Since 1950, however, the work has been expanding at an increasing rate and new research centers are being developed. Because of the specific requirements of soil dynamics research, future work will probably be conducted at these research centers where specialized research facilities and personnel can be concentrated. For example, results obtained from models are difficult to apply to full-scale equipment. Hence, apparatus is needed that can handle full-size equipment and large volumes of soil. The soil at these research centers is usually selected on the basis of its physical properties, and it is frequently moved to the center from great distances. Rarely are attempts made to reconstruct soil profiles; rather, uniform soil conditions are established to provide a homogeneous soil material. Special soil-fitting machinerv is required to establish and maintain specific soil conditions {351). Considerable improvement in this type of machinery is needed. Another requirement arises since accurate measurements can be made only when the device being examined is moved through the soil at controlled speeds, orientations, and depths while resulting forces are being measured. A track or guidance system, therefore, must be used to maintain a fixed path for the device throughout a test lane. Attempts to use portable tracks have not been successful, and more workers are resorting to fixed tracks. The fixed-track system is so specialized that it has little other use; hence, it must be used continuously for that purpose once it is constructed. Because of these factors, the facilities required in conducting the research are not only specialized but also very expensive. The result is that these facilities are constructed only when a long-range specialized program is to be pursued. Since no two of the existing research centers have facilities with the same capabilities, research on all types of problems cannot be conducted at every center. Specific problems may be handled better at one center than another. However, the willingness of the research agencies to cooperate to prevent needless duplication is most encouraging. 6 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Not all research utilizes full-scale equipment; smaller bins are often used for studies with small tools or models. Workers at many locations have small model equipment and their output of research data has been prolific. Small oins may be moved on tracks while the device to be investigated is held rigid. As the size of the soil bin increases, the tool is moved and the oin remains stationary. Limita- tations of speed and space are quickly encountered when small bins are used so that there is always a need to compromise between the size of the bin and the volume of soil that must be prepared. Be- cause the preparation of soil becomes a problem when the required volume increases, efforts are made to keep this operation to a minimum. A number of laboratories and organizations are engaged in research in soil dynamics. A description of several of these research centers is presented to show the type of research each is capable of undertaking. Actually, improvements and expansions at most of these centers are increasing their capabilities. 1.3.1 The National Tillage Machinery Laboratory, Auburn, Ala. The National Tillage Machinery Laboratory (NTML), a research facility of the Agricultural Research Service of the T^.S. Department of Agriculture, has 11 large bins of soil in which full-size wheels, tracks, vehicles, and tillage tools may be operated (fig. 1). The

FIGURE 1.—Soils varying in composition from sand to clay are contained in bins 250 feet long and 20 feet wide at the National Tillage Machinery Laboratory. Special measuring machinery operating on side rails permits only the device under study to be in contact with the soil. various forces acting on wheels or tools and the soil can be studied to determine the basic dynamic relationships and soil reactions. The soils vary in mechanical composition from sand to clay and provide SOIL DYNAMICS IN TILLAGE AND TRACTION < a wide range of soil material. The soils are prepared for tlie various investigations with specialized machinery, and moisture can be controlled to some degree by covering the plots or by watering them \yith a special mobile sprinkler apparatus. Indoor facilities provide better control of the environment for two large bins. Indoor laboratories provide facilities for emphasis on studies that do not require full-scale tillage and traction machinery. 1.3.2 The Army Mobility Research Center, Vicksburg, Miss. The Army Älobility Research Center, U.S. Army Engineers "Water- ways Experiment Station, conducts research to determine the trafficability of soil. Major emphasis is placed on soft soils where immobilization of vehicles or aircraft is likely to occur. A unique feature of the Center is an indoor small testing facility. As shown in figure 2, this facility utilizes an overhead set of rails

FIGURE 2.—Movable soil bins and dynamometer, at the Army Mobility Research Center, for determining the performance of normal-size wheels on different soils and soil conditions. Electrical signals generated by the detecting device are transmitted through instrumentation cables to recording equipment. (Photograph courtesy of U.S. Army Engineers Waterways Experiment Station) on which the test car is operated. The soil bins are fitted with the desired soil and then positioned under the guide rails during the test. Forces can be measured on wheels at speeds up to 25 m.p.h. A large indoor soil crushing and mixing plant is available for preparing soil so that measurements can be made on a continuous basis at any time of the year. This Center probably has the largest concentration of (1) personnel; (2) instruments for measuring, recording, and processing research data; and (3) supporting soil evaluation facilities for soil 8 AGRICULTURE HANDBOOK 316, U.S. DEPT. Oí' AGRICULTURE dynamics research. Research at the Center has covered many phases of soil-veliicle relations that are important in all types of ofï-the-road operations ( ^88 ). 1.3.3 The Land Locomotion Laboratory, Warren, Mich. The Land Locomotion Laboratory of the U.S. Army Ordnance Corps has pioneered in developing a land locomotion mechanics that emphasizes the physical relations between the morphology of vehicles ana the environment of their operation. Most of the work concerns off-the-road operations. Many of the studies are theoretical ; but with the aid of scale models tliey are frequently extended into experimental studies for verification of j)rinciples. A sunnnary of the re- searcli «¡¡proach and of some of the work that has been conducted at this Laboratory has been published ( 35, 37 ). The use of models, such as the one shown in figure 3, has reduced the time and expense

FIGURE 3.—A small model vehicle at the Land Locomotion Laboratory provides an economical means of studying soil and vehicle parameters. The characteristics believed to be of importance in land locomotion are being studied for many soil conditions. (Photograph courtesy of U.S. Army Ordnance Corps Land Locomotion Laboratory) of research in the dynamic relations between vehicles and soil. Arti- ficial soils have been used with the models to overcome some of the disadvantages of natural soils. Full-size experimental vehicles have been developed and evaluated at this Laboratory so that the overall soil-vehicle system can be studied. 1.3.4 The National Institute of Agricultural Engineering, Silsoe, England Research in soil dynamics is conducted at the National Institute of Agricultural Engineering without the use of large soil bins. Research in soil-implement relations has been studied with mobile testing units that can be used under field conditions. Figure 4 shows the dynamometer unit designed to measure tlie forces acting on tillage SOIL DYNAMICS IN TIIXAGE AND TRACTION

FIGURE 4.—A mobile dynamometer unit .it the National Institute of Agricul- tural Knglneerlng used to study the forces on tillage tools under dynamic operating conditions. The electronic signals produced by the measuring devices are recorded in an Instrument vehicle, which drives beside the test vehicle. (Photograph courtesy of National Institute of Agricultural En- gineering )

FIGURE 5.—The single-wheel tester at the National Institute of Agricultural Engineering used to determine the drawbar pull of wheels through a wide range of wheel slips. (Photograph courtesy of National Institute of Agri- cultural Engineering) 10 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE tools. Depth is controlled by small outrigger tracks, and this method appears to be satisfactory for a number of investigations. Tractive work is conducted with a versatile single-wheel tester unit, shown in figure 5 ( 310 ). The application of torque to the test wheel does not result in a load transfer to the wheel during operation. Both of these units may be used in the field without guide rails or tracks so tliat fixed control facilities are not recjuired. In addition, the units may be used in a variety of natural soil conditions; elaborate soil-fittmg equipment to duplicate natural conditions is not required. Considerable theoretical and experimental work concerning the forces acting on tillage tools has been conducted witli this type of equipment. 1.3.5 Institute of Fundamental Research in Agricultural Engi- neering, Volkenrode, Germany The Institute of Fundamental Research in Agricultural Engineer- ing of the Agricultural Research Center has conducted research concerning the forces acting on tillage tools. The mobile testing apparatus shown in figure 6 has been used in this research. The

FIGURE 6.—The mobile plow testing unit used by the Institute of Fundamental Research in Agricultural Engineering is shown with a disk plow in operating position. An auxiliary engine permits rotation of the disk during operation. (Photograph courtesy of Institute of Fundamental Research in Agricultural Engineering) apparatus is arranged so that the forces can be measured on a powered rotating disk as it is drawn through the soil. The forces acting on tillage tools operating in stony field soils can be measured with this unit. The power required to make certain basic soil cuts with individual rotary tiller tines has been determined by the use of model testing facilities in laboratory studies. Reports on basic studies of the forces acting on simple tillage tools have been a wel- come addition to the world literature. Both theoretical and experi- SOIL DYNAMICS IN TILLAGE AND TRACTION 11 mental work on stress distribution and soil compaction have been conducted at this Institute. 1.3.6. Institute for Agricultural Mechanization, Konosu, Japan Soil bins have recently been constructed at the Kanto-Tosan Agri- cultural Experiment Station at Konosu, Japan. The bins are now under the jurisdiction of a newly created Institute for Agricultural Mechanization. As shown in figure 7, these bins have many features

FIGURE 7.—The Institute for Agricultural Mechanization is equipped with six soil bins 150 feet long and 15 feet wide. The transfer car in the foreground is used to move the test machine from one bin to another or to the storage area. A single machine is used both for preparing soil and for conducting the tests. (Photograph courtesy of Kanto-Tosan Agricultural Experiment Station) of the bins at the National Tillage Machinery Laboratory, Auburn, Ala., including the tracks on which to oi)erate the measuring and soil- preparation machinery. A considerable amount of the anticipated research at this facility will be concerned with paddy-type soils. Studies have been made of the power requirements of rotary tillers, plows, and other tillage tools as well as of the traction and flotation of wheels, tracks, and vehicles. 1.3.7 Other Research Centers Many universities, experiment stations, and private and public research institutions are also engaged in research in soil dynamics, but the size of equipment that may be studied is limited. Individual agricultural engineering and soil departments have made numerous contributions, and many of these are described in chapters 3-8. Re- search work from isolated departments tends to be intermittent because it is not the main research objective of the department. Research is conducted by a number of conmiercial concerns and the development of special research departments for this type of work is increasing. Figure 8 shows some of the model facilities developed 12 AGRICULTURE HANDBOOK 316. U.S. DEPT. OF AGRICULTURE

FIGURE 8.-—A highly mechanized model testing apparatus used by the Cater- piller Tractor Company. (Photo courtesy of Caterpillar Tractor Company)

FIGURE 9.—A simple model apparatus at the National Tillage Machinery Laboratory used to determine soil reactions that occur around tillage tools. A glass side permits observation of underground soil reactions. SOIL DYNAMICS IN TILLAGE AND TRACTION 13 by the Caterpillar Tractor Company, Peoria 111. (78). The unit is completely mechanized so that the soil may be fitted automatically by a preset machine program. Not all model facilities are this large; few are mechanized beyond the movement of the soil or the device under test. One apparatus that has been used for a number of years at the National Tillage Machinery Laboratory is shown in figure 9. This type of inexpensive apparatus is an extremely valuable research tool when principles of simple systems are of interest. The numerous facilities indicate that a collective effort is under- way to enter a new era of research in soil dynamics. The applications of the various research agencies will differ, but work will be based on the same underlying principles. The need arises to assess our present position and to proceed in such a manner that fundamental knowledge is increased. Emphasis has been placed on securing practical answers, whereas the more basic aspects of problems have been neglected. A study of numerous reports concerning tillage and traction research indicates that failure to produce tangible results is usually traceable to the lack of information concerning fundamental parameters of the system. While there is need for information that can be applied to a solution of intermediate problems, more emphasis should be directed toward basic aspects of the problems. Continued effort must be made to coordinate research and to increase cooperative research in order to use the very special and excellent facilities available for soil dynamics studies. This would prevent the duplication of expensive control and measuring apparatus that might later remain idle because of limited applications by a particular research agency. The attitude and progress in this respect has been commendable, and it is becoming apparent that there is a mutual understanding and appreciation of the basic factors underlying diverse applications of the research information. 2. DYNAMIC PROPERTIES OF SOILS

2.1 Introduction The dynamic properties of soil are properties made manifest through movement of the soil. If a block of soil resting on a flat surface is moved, the resultant friction is a dynamic property of the soil; this property cannot be determined until movement occurs. Similarly, as loose soil is compacted, its strength increases; hence, strength is a dynamic property of soil. When soil moves, forces act that cause deformation or actual physical displacement. To describe the relations between the applied forces and resulting deformation, certain basic mathematical equations containing parameters are required. The parameters are measures of the dynamic properties of the soil. The structure or texture of soil is not a dynamic property. The structure may be changed as a result of movement, but it may be measured both before and after the movement. Such is not the case for dynamic properties. Studying dynamic reactions is difficult because the physical measurements must be made during the action. In addition, the insertion of measuring equipment into the soil mass may affect the soil reaction. The equipment may behave differently than the soil, if, for example, it is harder or softer than the soil. In spite of these difficulties, considerable progress has been made both in identifying dynamic properties and in utilizing these properties to describe the reaction of soil to forces {16). 2.2 Stress in Soil Describing forces acting in soil is not as simple as first appearances indicate. When discussing a finite block of soil, as in the case of sliding friction, vector representation of the gravity forces, me- chanically applied forces, and friction forces is probably sufficient. Even describing the distribution of forces within the finite block is not too difficult. When considering, however, that the mass of soil under discussion is usually a semi-infinite medium where the applied forces are distributed over a small finite section of the boundary, the problem becomes much more difficult. The concept of force per unit area becomes meaningless in a three-dimensional semi-infinite medium where neither direction nor a finite area is fixed. A method IS thus required to describe the forces acting at each point within and on the medium. The state of stress at a point is one method of describing forces within a medium. The method can be developed in a rigorous mathematical manner if the material is assumed to be continuous—that is, without any holes or gaps, unfortunately, the soil is not continuous since it has pores and is a granular material. The mechanics of the 14 SOIL DYNAMICS IN TILLAGE AND TRACTION 15 continuum, however, has been successfully applied to metals and fluids that appear as solids on a macroscopic level but that appear as mostly empty space on an atomic level. The difference between continuity of soil and continuity in a metal is thus a difference of degree rather than of quality. Since a finite area is required when dealing with a soil mass, either for measurements or for physical manipulation, the assumption of the continuum appears to be justified as long as the smallest area discussed is physically much larger than the pores or individual aggregates of the soil. The concept of stress has been successfully applied to soil by such workers as Bekker, Nichols, Payne, Soehne, and Terzaghi, ( 37,106, 829, 398, ^^7 )., By using stresses to describe forces in soil, each worker has assumed the continuum whether expressly stated or not. However, when extending the description to soils containing large pore spaces, in which the ratio of area under discussion to pore size is large, caution must be exercised to be sure that the description remains realistic. If an imaginary plane is passed through a body, the material on one side of the plane exerts a force on the material on the other side. If a small area Ù^A containing point O lying in the plane is selected, the vector sum of forces F acting on that area can be determined. The calculus limit of the ratio of F to AA when AA shrinks to zero is defined as the stress vector T at the point O associated with the plane, T = lim ^. (1)

For the limit to exist and have physical meaning, the area must be continuous ; hence, the mathematical requirement for the continuum. The stress vector T is usually broken into components normal to the plane and tangent to the plane. Although many methods are used to designate stresses, one common method uses the Greek letter sigma (er) for normal stresses and the Greek letter tau (r) for shearing stresses that are tangent to the plane. An appropriate subscript is generally used to indicate the plane with which each stress is associated. If another plane is passed through the same point O, usually a different stress vector will be found. Since an infinite number of planes can be passed through the same point some simple method is required for calculating the stress vector on any plane once certain specified values are given. It is possible to proceed along well-known lines established by the mechanics of a continuous medium ( 119, 190 ). Specifying the stress vectors on three mutually perpendicular planes is sufficient. Vanden Berg ( ^58 ) has pointed out that such a specification requires nine quantities and in this case represents an entity that is, by mathematical definition, a tensor. These nine components of a stress tensor at point O are shown in figure 10. Since graphically visualizing three intersecting planes is difficult, the normal representation embodies a small cubical volume element. The element is oriented with respect to a triad of orthogonal axes so that the sides of the cube are perpendicular to the axes. The components of stress shown are considered to be those that will be present when the volume of the element shrinks to zero at point O. 16 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE z i<^Z

^ ZX ^ ^

."^v ^v ^YX J^ ) '

FIGURE 10.—Normal and shearing stresses on a volume element.

To correctly describe the forces acting on and within soil, the nine values must be specified at each point including the boundaries. That the entity of nine values forms a tensor is in reality helpful, since the powerful techniques of tensor analysis become available to assist in solving the problem. Certain simplifications are possible. From symmetry and equilibrium, it can be shown that TX '7'xz — '7'z: and Tv By utilizing these identities, three of the unknowns can be eliminated so that only six independent values must be specified to describe the state of stress at one point in the soil. A property of the stress tensor is that the coordinate axes can always be rotated (and with them the imaginary planes bounding the cubical volume element) so that all shear stresses will be zero and only normal stresses will act on the three mutually perpendicular planes. The three normal stresses are the well-known principal stresses, and their directions are the principal axes of the stress state. The mean normal stress cr^ is defined as (Tm — 1/3 (cri + a-2 +0-3), (2) where CTI, 0-2, and era are principal stresses. The quantity is an invariant of the stress tensor so that the following relationship is also true o-^ = 1/3 (0-^ + 0-2,+o-z), (3) where (TX, o-y, and o-^, are the normal stresses referred to any coordinate axes of the stress state. A spherical state of stress is often discussed where each normal stress is equal to the mean normal stress— that is, similar to the stress state in water at rest. Subtracting the spherical stress from the total stress by appropriate mathematical methods leaves a deviatoric stress. The total stress state is thus mathematically separated into two components—spherical and devia- SOIL DYNAMICS IN TILLAGE AND TRACTION IT toric. In theories of elasticity and plasticity, spherical stress is generally associated with volume change; and deviatoric stress, with change in shape. Such an interpretation leads to convenient and often simplified relationships for describing behavior. 2.3 Strain in Soil The application of force to soil generally produces deformation or movement, or both. Just as the forces applied to soil must be described both within and on the soil mass, so deformation must be appropriately described. Unfortunately, the concept of a mathematical description of deformation is not as simple as the concept of stress used to describe forces. The usual procedure is to define strain at a point within a medium in sufficient detail so that the strain of any point in the neighborhood can be calculated relative to the chosen point. More than one value is required to fully describe strain at any point. Several approaches ( 182, 190, IfSO ) can be made to develop expressions for strain at a point, but all are based on the same principles. The position and lengths of line elements radiating from a point are described relative to the point after deformation has occurred. The change in the length of a line element is a measure of lineal or longitudinal strain. Longitudinal strain is defined as € = 4^, > (4)

where lo — initial length of a line element, I — final length after straining, e = longitudinal strain. For the expression to have physical meaning, the line element must be continuous; hence the assumption of the continuum is required to describe strain. Continuity assures the mathematical ^ correctness of using differential calculus to express longitudinal strain as d€ = f-, (5)

where de and dl are differential values of e and I as defined above. Another measure of deformation is the change in angle between two initially mutually perpendicular line elements. The usual definition (fig. 11) is y = tan (90°-i//), (6) where y = shearing strain, 90° — i// = deformation angle. As in stress, six independent values must be specified to define strain. Three mutually perpendicular longitudinal strains and three shearing strains in the planes formed by the triad of longitudinal strains are the required values. From these values, the longitudinal strain of any line element or the shearing strain of any two initially mutually perpendicular line elements radiating from the point can be calculated. These six independent values form a second order 18 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

/■ I I I I I I I ^-^P'

FIGURE 11.—Shearing strain defined as change in 90° — i//, the angle between two line elements.

symmetric tensor. Thus, a strain tensor similar to the stress tensoi is required to define the strain at one point. Unfortunately, the mathematical description of strain is not as rigorous as it is for stress. The line elements generally do not remain straight after straining; they become curves. The physical interpretations of the strain designations thus are erroneous. Fur- thermore, the definition of shearing strain is accurate only as long as the angular change between the initially mutually perpendicular line elements is small, since the tangent of the angular change is an approximation of the lateral movement of the end of the line elements in the plane containing the line elements. A finite strain theory ( 307 ) has been developed that will accurately describe deformation, but each component of the strain is a nonlinear expression of partial derivatives. Finite strain is thus so complicated that it is almost useless for practical purposes. Two simplifying assumptions that result in useful descriptions of strain have been made of the finite strain theory. The first and most widely used assumption is that the expressions for strain be restricted to small values so that the squares and products of the values can be ignored. This assumption leads to the so-called small strain or infinitesimal strain theory that successfully describes deformation in metals. For small strain theory to be accurate, strains must generally be restricted to values of less than 0.1 percent. The second assumption is that all straight line elements remain straight and all parallel line elements remain parallel. While such an assumption is not true over large areas, it is true in the immediate neighborhood of a point. The conclusions that can be drawn from these assumptions provide the basis for a relatively simple strain description called homogeneous strain. The usefulness of small strain theory can be extended to larger strains by redefining the incremental equation representing strain (equation 5) as ,- dl (7) SOIL DYNAMICS IN TILLAGE AND TRACTION 19 where ? is a common designation of natural longitudinal strain. The logic of the definition is reasonable since equation 7 states that incremental natural strain is equal to the incremental change in length divided by the instantaneous length being considered. In conventional small strain, the incremental change in length is divided by the original length, which is a constant (equation 5). Equation 7 can be integrated to give

= In -y-. (8) where I and lo are defined as in equation 4. Solving for l/lo from equation 4 and substituting in equation 8 gives € = In (1 + e), (9) which is the relation between the conventional and natural strain systems. By analogy, natural shearing strain is defined as y = In (1 + y), (10) where y is natural shearing strain and y is conventional shearing strain. Appropriate subscripts are usually assigned to the designations of strain in the various systems to orient the chosen directions for the line elements. Just as for stress, the line elements can be rotated at a point so that only longitudinal strains appear and all shearing strains are zero. These special directions are the so-called axes of principal strain and the longitudinal strains are the principal strains at the point. Dilation or volume strain in conventional small strain is defined as A = €i + €2 + €3 = €-1, + €j, + €^ (11) and in natural strain as A = €1 + €2 + es = €a; + Cy + €a (12) where subscripts 1, 2, and 3 refer to principal strains and a?, y, and s refer to any coordinate axes at the point. Using equations 4 and 9, one can show that equation 11 is an approximation of volume strain and is accurate only for small strains, whereas equation 12 is accurate for very large strains. To further illustrate the difference between conventional and natural strain, consider a bar of soil or some other material, as shown in figure 12. Length L represents the initial length of the bar and

B. C^ ^D I I -5L- -.5L- A- I I I ._L. . J

FIGURE 12.—A bar of material whose original length L was first stretched to AC and later to AD. 20 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE AC and AD represent two additional lengths to which the bar is stretched without failure. If the bar is strained to length J. 6^, conventional strain will be 50 percent ; and if the bar is strained to length AD^ the total conventional strain is 100 percent. If a second observer were to find the bar after it had been strained to length AC and he then strained the bar to AD, he would calculate conventional strain to be 33 percent. Since the first observer calculated strain to be 50 percent for the same deformation, the inherent inaccuracies of small strain theory are apparent. To be used with consistency, the entire history of soil would need to be known, but the entire history of soil can never be known. If the same bar is again considered by strains expressed in the natural strain system, both the first observer and the second observer will determine the strain to be 28.8 percent when the bar is stretched from AC to AD. The natural strain system thus appears to be much more suitable for describing large strains. While actual strains occurring in the soil may not be as large as 100 percent, they will certainly often be much larger than 0.1 percent. An increase in bulk density from 1.1 to 1.4 grams per cubic centimeter represents a volume change of 27 percent. In the so-called tillage range of soils, a change of 0.3 gram per cubic centimeter in bulk density is not unreasonable ; therefore, great care must be used when a strain theory is selected to describe deformation of soil. 2.4 Stress-Strain Relations Appropriate mathematical descriptions for stress and strain are only the first steps in describing the reaction of soil to forces. Con- sider for a moment the possible reaction of a granular material such as soil when it is subjected to mechanical forces. In general, the applied stress will be compressive. Vector addition of the stress over the boundary area will equal the applied forces. If the stress is small, the soil may deform slightly and reach an equilibrium condition through the storage of energy within the mass. Eelease of the stress will allow the soil to return to its original position. A larger compressive stress will produce enough strain so that a permanent deformation will result. Depending on the nature and condition of the soil, the yielding (permanent deformation) may result in a re- distribution of the load, a new and different state of equilibrium, or movement of the soil so that the load decreases or is no longer in contact with the soil. These possible reactions of the soil to applied forces can be described in mathematical relations between stress and strain. But the relations are generally so complex that only in special cases has enough knowledge become available so that accurate relations can be established. There is no logical way to calculate a stress-strain relation based on present knowledge of physical laws. All stress-strain relations have evolved from simple experiments where stress and strain are measured simultaneously. A mathematical formula is then determined to express the observed behavior, and this formula is extended to apply to generalized loadings. The best known and most successful stress-strain relation is the theory of linear elasticity. The basic premise of the theory is that SOIL DYNAMICS IN TILLAGE AND TRACTION 21 each of the six components of stress at every point is a linear function of each of the six components of strain at every point. Such a relation implies that 36 coefficients are involved. These 36 coefficients are parameters that are measures of the nature of the material and can be considered dynamic properties of the material. In the theory of elasticity, only 2 of the 36 parameters are mde- pendent if the material is Isotropie. An Isotropie material is one in which characteristics at every point are independent of direction. Since many metals are nearly Isotropie and their observed stress- strain behavior is approximately linear over a limited range, the theory of elasticity has been very successful in describing the relations between forces and deformations. Also, small strain theory is applicable since strains greater than 0.1 percent seldom are observed before nonlinear behavior occurs and permanent deformations result. The final step to complete the theory of elasticity is to develop a sufficient number of equations so a general problem can be solved. To illustrate, six unknown stresses and six unknown strains must be determined at every point; therefore, at least 12 equations are required to be able to solve for the unknown values. Six of the required equations are readily available from the six stress-strain relations. Equilibrium conditions lead to three equations relating stresses that must always be satisfied. Somewhat similar equations of compatibility on strain can be established to furnish the final three equations. The simultaneous solution of the 12 equations, together with boundary conditions, provides the solution to a problem. While the solutions are not easy except for simple loadings, the stresses and strains can usually be obtained. The solutions will accurately describe the behavior of any material that exhibits a linear relation between stress and strain—that is, isotropic-—and where the strains never exceed 0.1 percent. Unfortunately, soil exhibits none of the above characteristics except under very limited conditions. Several stress-strain relations describing so-called plastic behavior have been reasonably successful. They follow the general development of elasticity. The principal difference is in the actual stress- strain relation. Stress may be related to the time rate of change of strain, or to strain through a parameter that is in turn a function of the total strain that has occurred. One other difference between elasticity and plasticity is that the former predicts a deformation that is recoverable upon releasing the applied stress. The latter generally predicts a permanent deformation, although some recovery may occur in certain elasto-plastic materials. Again, as in elasticity, none of the presently available theories of plasticity adequately describes the behavior of soil. Soil deformation has a time-dependent property that is not recon- ciled by plastic and elastic theories. Since this is an observed phenomenon in soil, these theories are inadequate and must be discarded. McMurdie ( 280 ) has applied the theory of viscoelasticity to soil in a study of creep with some success. Although more work needs to be done to prove this theory, the theory provides an approach which considers time-dependent reactions and provides for a system with which to handle observed behavior in soil more realistically. Progress in developing stress-strain relations that adequately de- 22 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE scribe soil behavior has been delayed because of the wide range of soil and its behavior. The observed nonlinearity of stress-strain relations has yet to be mathematically described. Simplifying assumptions have been made to circumvent stress-strain requirements so that some degree of order can be made of soil reaction to forces. These approaches are discussed in detail in chapter 3. One must remember, however, that any approach not based on accurate stress- strain relations can only approximately represent the true behavior of soil. The development of suitable stress-strain relations, which in turn define parameters, is one of the more important areas of research in soil dynamics. Until such relations are determined, one cannot even study the dynamic properties of soil because they have not been clearly identified. 2.5 Soil Strength Soil strength is the ability or capacity of a particular soil in a particular condition to resist or endure an applied force. Soil strength might also be defined as the capacity of soil to withstand deformation or strain since strength is not evident without strain. The concept of soil strength is thus quite clear and easily understood. Soil strength is a physical quantity. The problem is to measure and describe strength so that a definite series of numerical values can be assigned. This problem has not been satisfactorily solved to date. The wide range of strengths observed in soils is one difficulty ; another is that the strength actually changes when force is applied and movement occurs. Changing strength is exhibited in many other materials but to a much lesser degree than in soil. Strength is thus truly a dynamic property of soil. One obvious way of describing soil strength is to use the parameters of stress-strain equations. The numerical values of the parameters for each condition would quantitatively describe its strength. Viscoelastic, yiscoplastic, and fluid mechanics equations are examples of stress-strain equations. Another way of describing soil strength is to evaluate the parameters involved in yield conditions. Yield conditions are fully discussed later in this chapter (sec. 2.8). Yield parameters are different from the two parameters, modulus of elasticity and Poisson's ratio, that appear in elasticity stress-strain equations. Accurate evaluation of the parameters of stress-strain equations and of yield conditions for soil provides a logical and sufficient means for describing strength. Lack of both stress-strain equations and adequate yield conditions for soil has prompted the use of simulation-type tests to describe soil strength. Some examples of these tests are discussed in chapter 3. The inability to describe soil strength accurately has dictated the kind of much of the experimental work dealing with soil dynamics. For example, tillage tools or traction devices can be compared only in the same soil conditions. Results obtained in one soil condition cannot be compared with those obtained in another soil condition. This is true even when the same soil type is used, because the strength may be different. The recent use of artificial soils ( 229, 2J4S, Slß^ 383 ) is an attempt to eliminate strength changes, so that a variable SOIL DYNAMICS IN TILLAGE AND TRACTION 23 can be studied with the assurance that strength is constant. Until soil strength can be evaluated, test results from one experimental location cannot be quantitatively compared with those from another location. The only valid comparison is between measurements made in the same soil condition. Indeed, soil conditions change with time —that is, climatic environment—so that in field studies where data are obtained over periods of days, test comparisons may not be valid even within one test period. Results may reñect changes in soil strength. One final word should be said about changing strength with loading. Such a phenomenon is not unique with soil since it is often observed in ductile metals after yield has been reached. The phenomenon has been referred to as strain or work hardening. In soil, strength increases as the soil becomes more compact. For stress- strain equations to be accurate, the changing strength must be included in the equations. In the tillage range of soils, loading causes large changes in volume so that changes in strength should be expected. Strength change is considerably larger than the strain- hardening effect in metals; furthermore, it occurs throughout the entire loading and not after a certain threshold value, such as the elastic limit, has been exceeded. Describing changing strength with load is thus highly important and may be one of the more difficult behaviors to describe in soil. More is said on this subject in the discussion of yield by compression. 2.6 Stress Distribution Transmission of stress through granular media is through the points of contact of the individual grains. Because of the random arrangement of the grains or particles, the points of contact do not form an orderly pattern except along a rigid boundary such as a ñat wall or ñoor. The contact pomts are thus randomly spaced in various directions. The stress transmitted through granular materials is, therefore, not in a straight line but in directions that are determined by the location of the contact points. This natural action of dis- tributing stress in granular materials has been termed arching. Before proceeding, let us reconcile the foregoing model to the model of the continuum that was assumed to define stress and strain. Certainly a medium where force is transmitted by points of contact is not continuous. Eecall, however, that stress and strain can be described realistically as long as the surfaces or areas being considered are large compared to the size of the gaps or holes— that is, a unit area has many points of contact from individual particles. The same problem occurs when describing stresses in metals. The structural engineer calculates forces in terms of stresses and in the process assumes that the material is continuous. The metallurgist, on the other hand, treats the same material as crystalline when he studies means of changing its strength, rigidity, machinability, or some other property. In reality, each area of behavior is represented by a different model, and there is no difficulty in reconciling the two models. Similarly, we can use a highly discontinuous granular model to help explain the behavior of soil and still assume continuity when mathematically representing its behavior. Many physical laws explaining 24 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the actions of the same phenomenon are based on different models— for example, the classical models of photons and waves, which represent light. Confusion and misunderstanding result only if each model is not kept separated from the others. Jenkin and others (200, 201, 313, J^OJf, 417-419) have studied arch action in simple systems in which the soil surface was moved and the mode of soil displacement noted, whereas others ( 105, 374 ) have developed theories about the nature of the arching phenomenon in uniformly uncemented particles in a plane, as shown in figure 13.

(A)

(B)

FIGURE 13.—A, Idealized nature of arching; B, vertical stress distribution for an idealized granular material. (Zelenin ( 515).)

The importance of the phenomenon is clearly demonstrated in a tunnel opening where the roof is supported from the walls. Since distributions are alw^ays required in a semi-infinite mass, the arching or vectoring out of the stresses is important. One wonders, however, if the arching phenomenon would have received as much attention as it has if a model other than a granular model had been visualized. The same phenomenon occurs in metals or plastics or nearly any other substance capable of withstanding a shearing stress. The phenomenon in such materials has been adequately represented by the distribution of stresses within the material. The important point, however, is that the distribution of forces in granular media cannot be represented by the concept of pressure, which is used in fluid media. The term stress rather than pressure should be used in soils, since pressure is usually identified with the state of stress in a fluid at rest. Under such a condition all normal stresses at a point are the same, and the pressure is identically equal to the mean normal stress. To describe the reaction of soil to a tillage tool or traction device, SOIL DYNAMICS IN TILLAGE AND TRACTION 25 the distribution of force on and within the soil must be determined. With adequate stress-strain relations the problem is simply to determine the stress distribution in the boundary area and obtain the simultaneous solution of the system of stress-strain equations. Lack of stress-strain equations has required other approaches to secure results for some immediate practical use. According to Taylor ( 4^21 ), Boussinesq in 1885 obtained a general solution of the elastic equations under a point load that was applied to a semi-infinite mass. In 1934, Froehlich ( 136 ) inserted into the distributions a concentration factor that alters the distribution according to the magnitude of the factor. The concentration factor also introduced varying soil strength into the equations. Because of radial symmetry under a point load, two of the three independent shearing stresses must be zero. Thus, only four stresses are required to specify the state of stress at a point. In cylindrical coordinates and assuming Poisson's ratio to be %, stresses are vP o-, = COS'' <^, (13)

vP (Tn = cos"""^ (^ sin^ <^, (14) ^TTT^

o-t = 0, vP Th = r^ cos''"^ (f) sin (^, (15) where v is the concentration factor and the other terms are as indicated in figure 14. Eotating the volume element about cTt axis so CTn

FIGURE 14.—Stresses on a volume element from a point load as defined in cylindrical coordinates. (Soehne, Agr. Engm. {401).) 26 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE plane is perpendicular to r—that is, a polar coordinate system—reduces the stress system to cr^ and all other stresses are zero. These are the principal stress axes and (Jr is given by vP cos"-^ 0. (16) 2TTr Soehne ( ^01 ) assigned different values to v for soils in various conditions and calculated the stresses under tractor tires. These distributions are discussed in chapter Y. The v values used were 4, 5, and 6 for hard, medium, and soft conditions, respectively. The larger the value of v^ the more concentrated the distribution along the load axis (fig. 15). One must keep in mind, however, that the

f/ù,^:^///Jk^/??

FIGURE 15.—Calculated principal stress distributions (cr) in soil under tires: Left, Hard soil; center, medium soil, and right, soft soil. (Soehne, Grund- lagen der Landtechnik ( 395 ). ) distributions contain the inherent assumptions of linearity between stress and strain, strains less than 0.1 percent, and isotropy. The v factor merely modifies the general shape of the distribution and does not, in fact, represent a measured soil parameter that has a true physical significance. Also, a point load is never applied to the soil, and rarely does the assumption of a point load even reasonably represent the true situation. Great caution is required if equations 15 and 16 are used to calculate stress distributions in soil. Other approaches have been used to calculate stress distributions in soil. Civil engineers have often assumed that soil under footings behaves as an .elastic material, and they used solutions of the elastic equations. Love in 1929 ( 256 ) obtained solutions to the elastic equations for uniform circular loads applied to a semi-infinite body. An attempt to simplify these equations for easier computations was made by the Waterways Experiment Station ( ^78 ). Yield conditions imposed on soil by tillage tools have been assumed and stress distributions implied from the geometry of the loading. Examples of this technique are discussed more fully in chapter 4. One final method that merits discussion is based on the techniques SOIL DYNAMICS IN TILLAGE AND TRACTION 27 of limit analysis. Mathematicians have proved that only one solution is possible for a system of stress-strain equations and, hence, a unique applied load exists for the solution. Also criteria have been established that assure that a distribution will give loads that are above and below the unique load. Distributions are assumed to satisfy the appropriate criteria, and the associated loads are calculated to bracket the final solution ever closer. When the loads above and below the unique load are reasonably close, an approximation of the correct answer is provided. This technique was applied successfully to a study of the stability of earth walls by Murnaghan ( 307 ). None of the foregoing approaches seem to be accurate enough to adequately describe the observed stress distributions in soil ; improvements in these methods or new methods have to be developed. The direction and magnitude of stress in soil may be measured by placing on or in the soil a sensing device that can detect the stress. Many types of stress transducers and similar devices have been designed for this purpose ( 90^ 157^ 395 ). Many have been used successfully to measure stress distributions through highway fills, under tractor wheels, and under compacting rollers. The electrical resistance strain gage developed after World War II permits the most successful design of sensing elements. Numerous transducers of this type have been described and used ( 13, 83,175, 333, 337, 3^6, Ui, ^78, 481 ). Two principles have been used in constructing most of these transducers. Figure 16, A shows a type of transducer in which the FLUID CHAMBER i_z SENSING DIAPHRAGMV ^ INSTRUMENTED DIAPHRAGMJP^sJ^ INSTRUMENTED DIAPHRAGIiM^

j ^j jj/^jjjj^jj U??? ? ? ?^ ?j ?j j? rr ///////^//^j'

•STRAIN GAGES'

(A) (B>

FIGURE 16.—Stress transducers instrumented on A, secondary and B, primary diaphragms.

force applied over a known area is transferred uniformly to an instrumented diaphragm by a fluid pressure. Figure 16, B shows an instrumented diaphragm where the load is applied directly to the diaphragm. The amount o-f flexing of the instrumented diaphragm in each transducer is interpreted in terms of applied stress. Only the normal stress on a transducer is measured. The sensing surface of a transducer represents a plane, and a stress vector acts on the plane. Most transducers designed to date are insensitive to shearing stresses and so respond only to the normal component of the stress vector. One problem in using stress transducers is to follow their orientation, particularly if large deformations of the soil occur and the transducer rotates. With an adequate description of movement of the transducer, corrections can be calculated. 28 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE The main problem in designing stress transducers has been to overcome the effects of the arching phenomenon. If the transducer is more rigid than the surrounding soil, a higher value will be obtained than if the transducer has the same rigidity as the soil. Set- tlement of soil immediately adjacent to the transducer results in arch action that transfers some of the applied load to the transducer, as shown in figure 17, A. Conversely, if the transducer is less rigid

CELL CELL (A) (B)

FIGURE 17.—Possible interactions that give erroneous stress readings. than the soil, a lower value will be obtained since the load will be transferred from the transducer to the surrounding soil, as shown in figure 17, B. Thus the size, shape, and resiliency that the transducer presents to the soil mass will affect the transducer's reading. Within certain limits, the transducers appear to give valid readings. A diameter-thickness ratio of 5:1 appears to give satisfactory results for circular transducers, although ratios as low as 2:1 have been used. Although no definite evidence has been presented, the exact ratio is probably a function of the degree of soil settling during loading and the closeness of the transducer to some firm object or layer in the soil. No transducer has been devised that can make measurements without some degree of disturbance to the soil, but use of transducers in snow ( 4^0 ) shows that the degree of disturbance may not preclude their profitable and reliable use until better transducers are devised. Improved instrumentation will permit studies of stress distributions that heretofore could be evaluated only from empirical calculations. Certain stress indicators may be used to qualitatively determine stress distribution in soil. Since compaction is caused by stress, the density of soil increases as stress increases. The location of compacted areas after loading a homogeneous soil is, therefore, an indication of a stress concentration. In snow studies, the "Nakaya Pit Burning" technique ( 309^ 4^5^ JßO ), where smoke from an oil fire deposits more carbon on denser snow, employs this principle so that compacted areas can be detected. Materials that require small SOIL DYNAMICS IN TILLAGE AND TRACTION 29 strains for fracture—that is, stress coats—can be used in only rare cases. Similarly, pliotoelastic techniques have highly limited applications in soil because of the extreme porosity of the soil, the influence of the material on soil strenjith, and the large strains resulting from yield. A soil box with one side made of thick glass plate has been used at the National Tillage Machinery Laboratory to locate stress concentrations. Reaction of the soil to a tool can be viewed through the glass side. The tool is moved through the soil immediately parallel to and against the glass, and the compacted areas are located visually. The stress concentrations are obvious in some soils, as shown in figure 18.

FIGURE 18.—Stress concentrations inferred from soil reactions observed through a glass-sided box.

2.7 Strain Distribution Very little effort lias been made to determine strain distributions in soil. The obvious means of obtaining strain distributions is to solve representative stress-strain equations. Emphasis has not been placed on other means of determining strain distributions, as it was for stress, because the boundary conditions imposed on soil are more easily expressed in terms of forces. Furthermore, most yield conditions are based on stress so that stresses are much more useful than strains. Several attempts, however, have been made to measure strain m 30 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE soil. Woodruff ( 509 ) buried a simple elevation rod in the soil to measure the vertical strain caused by shrinkage of the soil during drying. Workers at the Waterways Experiment Station ( ^80 ) have used linear deflection gages to measure strain in large masses of soil subjected to heavy loads. Hendrick and Vanden Berg ( 181 ) measured dynamic strain on small briquettes of soil subjected to uniaxial tension. Gliemeroth ( 155 ) used a photographic technique to measure the displacement of soil particles under moving vehicles. His method, shown in figure 19, consisted of digging a pit along

fwh-n DIRECTION OF TRAVEL

(A) (B)

FIGURE 19.—Path of displacement of a soil particle under a vehicle recorded photographically. (Gliemeroth, taken from Ztschr. f. Acker und Pzlanzenbau 96: 225. 1953. Verlag Paul Parey, Berlin and Hamburg {155).) the proposed path of the vehicle so that the soil was exposed in a small area under the path. A movie camera in the pit recorded the displacement of a marker in the soil as the vehicle passed over the site. Strain may also be measured on a volumetric basis under dynamic loadings. Hovanesian ( 185 ) devised a volumeter utilizing a balloon filled with soil, which was buried in a larger mass of the same soil. The balloon opening was connected to a horizontal pipette containing a drop of mercury that acted as a rolling seal. The soil inside the balloon was assumed to act in the same manner as the surrounding soil, so that it represented a small volume element of soil. Any volume change inside the balloon forced air from the balloon into the pipette and displaced the mercury seal by an amount equal to the volume change. If the initial volume of soil inside the balloon is not known, the final volume can be determined by water displacement after the volumeter is removed from the soil. A slight vacuum applied to the balloon insures that the final configuration of SOIL DYNAMICS IN TILLAGE AND TRACTION 31 the compacted soil is maintained. The volumeter is sensitive to temperature, however, so that it must be used under isothermal conditions. The volumeter was later modified { 186 ) to obtain an electric signal that could be recorded. Figure 20 shows the components of the original volumeter as well

FIGURE 20.—Volumeter provides a measure of soil compaction by measuring the volume of air displaced from a soil-filled balloon. (Hovanesian and Buchele, Amer. Soc. Agr. Engin. Trans. ( 186 ).) as the transducer used to make the volumeter recording. A sensitive stress transducer measures the increase in pressure in a closed system. The volume change of saturated soils has been measured by collecting the outflow of water from the triaxial apparatus. Vanden Berg ( JfßS ) utilized the volumeter principle with appropriate temperature control to measure air outflow in unsaturated soils in triaxial apparatus. Most investigations of strain have been confined to small volumes of soil where static movements and measurements were made. Dis- tributions have not been determined in complex systems, primarily because of difficulty in instrumentation. Measurement of principal stresses and principal strains completely defines the forces and deformations of the system. Simultaneous measurement would permit studying stress-strain relations. Much research, therefore, remains to be done in the area of stress-strain measurements. 2.8 Yield in Soil The wide range of behavior of materials found in nature contributes to possible confusion concerning the definition of yield. Be- cause of the importance of ductile metals in the world, their behavior has been more widely studied than has the behavior of other materials. Many of the concepts and terms that originally described behavior of metals are confusing when applied to other materials. A typical stress-strain curve of a ductile metal subjected to uniaxial tension is shown in figure 21. For low stresses, if the stress is reduced to zero, the strain will also return to zero and no permanent deformation will occur. The straight line portion of the curve 32 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

CO (O UJ

STRAIN (€)

FIGURE 21.—A typical stress-strain curve for a ductile material. represents the elastic region where behavior is adequately described by the classical theory of elasticity. Loading beyond the elastic range results in a permanent deformation, and it is in this region where theories of plasticity attempt to represent behavior. For ductile materials, the stress CTO where permanent deformation first appears is defined as yield. In many designs utilizing ductile metals, the yield stress is considered the failure stress or highest stress that can safely be carried by the metal. The stress cr^ is the familiar ultimate stress—the value that produces fracture or separation. Brittle materials differ from ductile materials in that fracture usually occurs as or just after the yield stress is reached so that very little plastic behavior is exhibited. Yield is, therefore, some point of failure that is of interest in the stress-strain regime of the material. Different types of failure or more than one criterion of failure may be of interest for any one material, depending on one's interest in the reaction to forces. Failure in soil is much more complex than in metals or most brittle materials. This complexity has led to confusion and misunderstanding concerning yield in soil. Since soils found in nature vary from a near liquid to a brittle material, the confusion is understandable. A complete description of the reaction of soil to an applied force involves not only stress-strain distributions but also yield conditions. If stresses or strains exceed the yield values, the soil deforms so that stresses are redistributed, or the load is decreased, or the soil becomes stronger so that yield is no longer exceeded. Four types of failure for soil can be defined in terms of stress-strain behavior: shear, compression, tension, and plastic now. 2.8.1 Shear A pictorial concept of stress at a point will be useful in an attempt to define shear failure. As discussed in section 2.2, the stress tensor defines the state of stress at a point. To graphically describe a state of stress, Mohr's circle provides an elegant representation in two dimensions. Jaeger ( 190 ) has reviewed Mohr's work to show how the two-dimensional idea has been generalized to three dimensions. SOIL DYNAMICS IN TILLAGE AND TRACTION 33 The concept in three dimensions is to describe the normal and shearing components of the stress vector that acts on all possible planes passing through a point. While the mathematical derivation of this representation is too involved to present here, the description simplifies to plotting in two dimensions the magnitude of the normal component against the magnitude of the shear component. The plot of all such points for a particular stress state will cover some specific area. The shape of the desired area can be described if the principal stresses are known. Arranging the principal stresses so that CTI represents the algebraically largest principal stress and o-m represents the algebraically smallest principal stress, three circles can be constructed as shown in figure 22. The crosshatched area represents the

FIGURE 22.—A two-dimensional representation of a stress state in which the shaded area represents the stress vector on all possible planes at the point.

desired area to describe the stress state. Note that if any two of the principal stresses are equal, the three circles become one and the area becomes the circumference of one circle ; the one circle is Mohr's representation in two dimensions. Maximum shearing stress, largest principal stress, and other stresses can be easily obtained from the graphical representation of the state of stress. Failure by shear has a clear meaning for brittle materials. The classical example is the brittle-type shear fracture that develops when a solid cylinder of material is loaded in compression as shown in figure 23. This type of failure is also observed in soil. A similar type of failure is observed in some soil conditions where no definite fracture occurs but where the diameter of the specimen under test gradually increases with load. The stress state that causes fracture or incipient plastic now—that is, larger diameter and hence permanent deformation—is a measure of shear failure. The definition of failure by shear is thus some function of the stress state that just causes the failure. In soil, both complete fracture and incipient plastic flow have generally been indicated by the same stress function. A review of shear by Jaeger ( 190 ) indicates that the first theory 34 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

FIGURE 23.—A brittle-type shear failure develops where a cylinder is failed in axial compression. to predict shear failure dates back to Coulomb. He proposed that failure occurs when the maximum shear stress reaches some critical value. This value by our terms of reference would be a dynamic property of the material. Navier, as reviewed by Jaeger ( 190 ), modified the maximum shear stress theory to a form that qualitatively fits more facts than the original Coulomb theory. Navier proposed that shear failure occurs on a plane where the shear stress reaches some constant To that is increased by a constant factor /x times the normal stress cr (compressive) acting on the plane. If cr is defined as positive when compressive (the normal procedure for soils), the criterion becomes To + /XO-, (17) where \T\ indicates the absolute value of the shearing stress to cause failure. As figure 22 shows, there are two possible planes of failure at each stress state where cr and r have the same absolute magnitude but T has a different algebraic sign. In reality the sign is immaterial with regard to actual behavior since the sign indicates the direction of failure but does not change the condition for failure. Mohr, according to Jaeger ( 190 ), also proposed a shear failure theory ; he argued that cr and r on the plane of failure are connected by some functional relationship. If a series of different stress states that just cause failure are imposed on the same material and these stress states are plotted as Mohr's circles, as in figure 22, the envelope that is tangent to the circles represents a failure criterion since any stress state whose circle touched the envelope would be at shear failure. The simplest envelope to describe mathematically is a straight line, and under this representation Mohr's criterion is identical with equation 17. Figure 24 shows a Mohr envelope where posi- SOIL DYNAMICS IN TILLAGE AND TRACTION 35

FIGURE 24.—A Mohr envelope of stresses from which soil parameters TO and 0 can be determined.

tive a is again considered to be compressive. The constant /x of equation 17 is equal to the tangent of (/> where (/> is the angle indicated in figure 24. The constancy of the ratio r to or is the same as the Coulomb concept of sliding friction so that the angle (j> is otten visualized as the angle of internal friction. The constant r, has been called cohesion and is usually represented as G m equation 1« T = Í7 + 0- tan (/), (18) where 0 = cohesion, (f) = angle of internal friction, cr = normal stress, T = shearing stress. Cohesion has been rationalized as the shear stress at zero normal load. While the straight line envelope of the Mohr theory does not rigorously represent shear yield in all soil conditions, the theory has been close enough to experimentally observed behavior so that equation 18 has been almost universally accepted as a law. One confusing factor is that G and (j) are so firmly entrenched that they are often referred to as real physical properties of the soil, in reality they are only parameters of the assumed yield equation. Their logical existence can be explained only by an interpretation of the equation and not from the physical nature of the soil itselt. Another confusing factor has been the tendency to mix the distribution of failure points in a soil mass with the criterion itselt. Equation 18 represents shear failure at one single point, but the representation suggests failure on a plane. Shear plane as a description of the failure is, therefore, logical terminology. In a distribution of failure points, as shown in figure 25 by the sharp ]0g in the strings, a failure surface is indicated. Unfortunately, this failure surface can often also be represented by a plane so that shear plane has been applied to the surface. Care must be used to keep the criterion for shear separated from the distribution of shear point failures. The former is clearly represented by a plane, whereas the latter is a surface that can have any shape. 36 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

_>(fl*iin?wT.

FIGURE 25.—Shear failures in front of a simple tillage tool, as viewed through a glass-sided box.

Two methods have been used to measure failure by sliear in soil. Both methods attempt to obtain quantitative values for the C and <^ of equation 18. In the simpler of the two methods the failure surface is controlled over a small area of soil, and shearing stresses are measured for several normal stresses on the failure surface. These values are plotted directly on a T, cr coordinate system. The line connecting the points is an envelope and C and ^ can be read directly. The devices used for these determinations fall into the general category of direct shear, and several devices are discussed in chapter 3. In the other method for determining shear failure, various stress states are applied to soil and a series of Mohr's circles that represent shear failure are determined. The envelope to the circles again permits determining C and ^. The most widely used method of obtaining Mohr's circles at failure is with triaxial apparatus, which is discussed in chapter 3. 2.8.2 Compression Failure by compression in soil has generally been associated with volume change. In metals, volume changes are usually so small they can be ignored, but in soil, these changes cannot be ignored. Com- j)ression failure in soil should.not be confused with compression failure in metals, which is generally defined as the value of uniaxial stress in compression that causes failure. Most often this value is assumed to be equal to the ultimate stress o-„ in tension (fig. 21). Data which indicate that these are not the same for soils are shown in table 1. SOIL DYNAMICS IN TILLAGE AND TRACTION 37

TABLE 1.—Tensile and compressive strengths of two soils

Tensile Compressive Ratio : Tensile strength/ Type of soil strength strength Compressive strength Cecil : P.s.L P.SÀ, Sample 1—. 52 86 0.60 Sample 2__. 51 125 .41 Hagerstown : Sample 1—. 135 342 .39 Sample 2__. 182 357 .51

SOURCE : Winterkorn { 508 )

For our purposes, failure by compression in soil is defined as the state of stress at incipient volume change. The observant reader will immediately question such a definition. As shown in section 2.2, the magnitude of six components of stress must be determined to define the state of stress. Equations 11 and 12 imply that volume strain can be accurately described by specifying the magnitude of only one number—the dilation. The task of mathematically equating the six components of stress to one value for strain suggests some functional relation. More precisely, a stress-volume strain relation is required. Thus, the concept of compression failure, while logical, requires a stress-strain relation that has never been established. As a result, simplifying assumptions have been made to describe the behavior. Confusion occurs if the behavior is considered only as a stress-strain relation since it is also a criterion for compression failure. Confusion also occurs if failure by shear and failure by compression are considered as two separate phenomena. Their behavior in nature is some combined action, and any mathematical representation that separates the action into two parts can be questioned regardless of how rigorous the mathematics may be. The representation of failure by shear and by compression as separate criteria is valid only as long as behavior can be adequately described. Data in chapter 4 indicate that the two yield conditions are not independent. Until compression failure and shear failure are more completely described where they are considered as one combined phenomenon, yield in soil cannot be adequately described. Measurement of compression failure, of course, varies with the assumed stress-volume strain relation. These relations are discussed in chapter 3. Usually the procedure involves placing soil in some type of confined container where the volume can be accurately determined. The assumed function of the applied stress states is determined, and generally the resulting percentage of pore space or bulk density is associated with the stress function. A series of such determinations gives a criterion for yield by compression. 2.8.3 Tension Failure by tension has the same meaning in soil as in metal. Thus, the ultimate tension CTU shown in figure 21 also represents tension failure in soil when complete separation occurs. Expressing tension failure in precise terms is difficult because of the porosity of soil. The problem is to describe the area over which the force acts. The 38 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE total area (air, solid material, and water), the area of solid material and water, and the area of only solid material have all been used for this purpose. Using any area other than total area is an attempt to incorporate behavior explained from a granular model into the mathematical model of the continuum. As pointed out earlier, this technique is not inconsistent and does not violate either model. The area to use should be the one that results in the best representation of tension failure. The Mohr envelope of stresses (fig. 24) also indicates tensile stresses. Along the ordinate, stresses to the left of the abscissas are tensile stresses and those to the right are compressive. Willetts ( 50p ) has constructed the locus of shearing stress r from a combination of measured values of tensile and compressive stress loadings that were imposed to cause soil failure. When uniaxial tensile stress is applied to cause soil failure in a rigid body system, there should be no shearing stress. When soil does not act as a rigid body, the behavior induces shearing stresses. Accordingly, a shearing stress r will accompany each tensile stress cr. Vomocil and Waldron ( Ii.68 ) have studied Mohr relations in which the shearing stress was less than To^ In this case, the magnitude of the shearing stress may be calculated from the ratio of the negative major to minor principal stresses and the angle of internal friction. Direct tension is seldom applied to soil by a tillage tool or traction device. Tension failure does have physical significance, however, and may sometimes be induced during soil manipulation. Although soil is often thought to be incapable of sustaining a tensile force, its tensile strength may be very high. Table 2 gives tensile failure

TABLE 2.—Tensile strengths of several soils

Type of soil Tensile strength Source P.SÄ. Cecil clay 65 Winterkorn {508). Hagerstown clay 160 Do. Putnam silt loam 188 Do. Houston clay 354 National Tillage Machinery Laboratory ( Sll ). Hiwassee sandy loam 61 Do. Lloyd clay 100 Do strengths of several clay and loam soils. The soils were dry and cemented; their strength decreased rapidly on wetting. Neverthe- less, the values indicate that soil can be strong in tension. The.shear criterion for failure (equation 18) implies that soil strength is composed of two factors—cohesion and friction. Cohe- sion is defined as the force that holds two particles of the same type together. When soil fails in tension, only the cohesive part contributes to resistance since the normal stress is zero. Such reasoning immediately suggests that tensile failure may be exactly the measure of cohesion. Unfortunately, no one has yet devised a means of measuring direct shear at zero normal stress so the question has never been resolved. In reality the argument is of academic interest only SOIL DYNAMICS IN TILLAGE AND TRACTION 39 since cohesion at zero normal stress is a "mathematical property" of soil and not a real physical property. Measurement of tensile failure is relatively simple since it involves applying a uniaxial stress state across some known area. The various techniques and apparatus are discussed in chapter 3. Most tension measurements have been made on briquettes of soil formed by various methods. The most useful aspects of tension failure are the simplicity of the measurement and the ease with which laboratory control can be maintained in forming briquettes for test. In the applied stress state at tensile failure, all components of the stress tensor are zero except one normal stress ; tensile failure is thus the simplest application of forces that can be made to soil. Thus, failure can perhaps be determined with less interaction of apparatus and soil so that an intrinsic dynamic property of soil is determined. Tensile failure appears to be an excellent means for studying some factors that affect soil strength. It must be remembered that tensile tests establish a single point on the yield surface and that they do not provide information regarding the form of the yield surface and its dependence on strain history. 2.8.4 Plastic Flow The phenomenon of plastic flow in soil has never been clearly defined. One example of the action termed plastic flow is observed when a subsoiler moves through a wet clay. Instead of shattering and developing shear failure surfaces, the soil flows around the subsoiler and remains essentially a continuous mass with only a cleavage plane where the subsoiler has passed. For this action to occur, presumably the soil must fail in shear so that it can deform—that is, strain—but no clearly defined failure surface develops. Eather, the entire mass in the immediate neighborhood of the applied forces fails by shear but does not strain to the degree that complete separation occurs at any point in the mass. If the state of stress on a volume element of soil is examined at plastic flow failure, equation 18 can describe the yield stress condition even though failure does not occur on a definite plane. Thus plastic flow (failure) can be defined in terms of shear failure even though the physical action involved is vastly different. Until stresses that cause plastic flow can be measured quantitatively and a criterion for plastic flow failure can be evaluated, plastic flow yield cannot be rigorously defined. 2.9 Rigid Body Soil Movement Our discussion so far has concentrated on forces and deformations within the soil mass. Many actions occur in tillage where finite portions of soil can be considered to move as a rigid body. For example, a large clod of soil thrown by a moldboard plow can be represented by a rigid body of soil where internal forces can be neglected. The equations involving properties of soil such as friction, adhesion, and abrasion describe the movement of a rigid body of soil with respect to some other material. These descriptions are much simpler and further developed than those involving stresses within the soil mass. Unfortunately, the action of a complex tillage tool such as a non- 40 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE scouring moldboard plow involves both rigid and nonrigid body descriptions; often the same mass of soil is involved in both descriptions. This double involvement is complicated but justified since we are using different mathematical mode^ls to represent only the observed behavior. 2.9.1 Momentum Momentum does not involve a dynamic property of the soil but is often involved in the action of tillage and traction equipment. Mo- mentum is the product of mass and velocity. Since a rigid block of soil has a definite mass and when moving has a definite velocity, its momentum can be defined. If properly utilized, this momentum can have considerable inñuence on soil breakup. Besides describing the momentum of a rigid block of soil, the Newtonian laws of motion rigorously represent such factors as forces, accelerations, velocities, displacements, and inertias. Thus, a mechanics of detached soil masses is available and is clearly defined. The inherent assumption when using Newtonian laws is that the mass being considered behaves as a rigid body. 2.9.2 Friction When two rigid bodies of soil move with respect to each other, forces act on the mutual contact surface. The general laws of Coulomb friction apply, but the exact nature of frictional forces is not yet known {80). The usual procedure is to separate the acting forces into those normal to the surface and those tangent to the surface. Following Coulomb's concept, a coefficient of friction can be defined F /^ -^ = tan i/;, (19) where F = frictional force tangent to the surface, N = normal force perpendicular to surface, fjL = coefficient of friction (soil on soil), ifj = angle whose tangent is /x, as shown in figure 26. To move the upper block of soil, a force must

FIGURE 26.—Normal force and friction force between two rigid bodies of soil. be applied. The magnitude of the applied force must exceed F before movement starts, so that /x is a parameter of the equation relating forces during the movement of one rigid body of soil over another rigid body of soil. The coefficient of friction /x is thus a dynamic property of soil. SOIL DYNAMICS IN TILLAGE AND TRACTION 41 The coefficient of friction /x in equation 19 should not be confused with the tangent of the angle of internal friction ^ in equation 18. Equation 18 with C equal to zero is exactly analogous to equation 19 if tan ^ is equated with /x, and F and N are expressed on a unit area basis; but the two equations represent different phenomena. Equa- tion 18 represents incipient shear failure within a soil mass. After failure has occurred, the fracture surface separates the mass into two distinct masses. These two masses can be depicted as rigid bodies, and movement of the bodies relative to each other along the surface is represented as sliding friction by equation 19. The two mathematical models are thus completely different, and one would not expect the two friction values to necessarily be the same. Unfortunately, both i// and ^ are usually determined experimentally by the same general procedures so that they cannot always be clearly separated, and confusion often results when an attempt is made to apply the values for design purposes. Equation 19 represents sliding of soil, and within limits this process can be represented as simple friction. Experimentation has shown that /x is: (a) independent of normal load; (b) independent of the area of the surface; (c) independent of the speed of slipping. None of the conditions is completely true for soil, but they represent observed behavior closely enough so that they are applied unless very large normal loads or speeds are involved. Determining when complete separation occurs and rigid body movement begins is perhaps the most difficult problem in using equation 19. The coefficient of friction is frequently measured by means of a simple box, as shown in figure 27. The entire normal load on the

V///////

FIGURE 27.—A method for inducing direct shear failure along a predetermined surface.

soil is transmitted through the soil. Shims are placed between the upper and lower parts of the box during filling. Eemoving the shims for measurement assures the necessary clearance. Failure occurs between the two halves of the box so that F in figure 27 is equivalent to the frictional force. If the coefficient of friction is considered to be independent of normal load, a series of different normal loads plotted versus the frictional force gives a straight line. The slope of the line is a measure of the coefficient of friction /x. Nichols ( SIS ) and others ( 12 ) have measured shear failure on two surfaces as the central portion of a cylinder is moved. There appears 42 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE to be no disadvantage to this method (fig. 28). Values for the coefficient of friction have been found to be between 0.2 and 0.8.

FIGURE 28.—Direct shear measured along two cylindrical surfaces.

Frictional forces do not occur only between two rigid bodies of soil ; they may also occur between soil and some other material. In tillage tools, the material is usually steel but may be plastic; in wheels or tracks, it may be rubber. The coefficient of friction between soil and a material is determined in essentially the same manner as shown in figure 27 except that a slider of the material replaces the upper portion of the box. To distinguish the difference in the coefficient, the coefficient may be subscripted /¿ to indicate that it represents a soil-material coefficient. The coefficient of friction between soil and other materials is subject to the same general laws of friction previously discussed. A number of factors affect the coefficient and these will be discussed after the concept of adhesion has been developed. 2.9.3 Adhesion Among the forces acting in the mutual contact surface of two rigid bodies of different material is a force often required to pull the two bodies apart. The force results from an attraction between the two unlike materials and is defined as adhesion. Between soil and some other material, adhesive forces are almost exclusively due to moisture films. Moisture tension and surface tension of the soil solution appear to explain the behavior of adhesive forces. Surface tension is related to adhesion through the familiar capillary equation that represents the rise of a solution in a capillary tube. The height of rise is determined by , 2r cos a h = , (20) g p r ^ ^ where h = height of rise, T = surface tension, g = acceleration of gravity, p = density of solution, r = radius of capillary tube, a = contact angle. SOIL DYNAMICS IN TILLAGE AND TRACTION 43 The concept of theoretical maximum radius is useful and is based on the fact that the angle of contact (wetting angle) is constant. Both theory and observation indicate that the meniscus in a capillary tube is approximately spherical. Figure 29 shows the relation between

FIGURE 29.—The curvature of a capülary film as related to the wetting angle. the radius of the tube r, the angle of contact a, and the theoretical maximum tube size R. The theoretical radius R is determined by the spherical section of the meniscus, which in turn is determined by the angle of contact, and R is interpreted as the maximum radius tube that a given surface tension could support ; that is, r can theoretically be increased to i?. The geometry in figure 29 shows that

cos a = (21) R' and substitution of equation 21 into equation 18 yields 2r h = (22) pgR where R is now the radius of the theoretical limiting tube size or pore size that a given surface tension will support. Since the term A p ^ is a pressure term and gives a measure of pressure, equation 22 can be written P -^ (23) ^ ~~ R' where P is now pressure in the continuous solution. Since h in equation 20 represents a pressure deficiency—that is, less than atmos- pheric pressure—F in equation 23 is the basis for using moisture tension measurements as a means of measuring pore size distribution in soil. As the moisture tension is increased by some means such as a moisture tension table ( 192 ) or a pressure membrane device 44 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE ( JfJfS ), the soil pores will support the tension until the capillary force is overcome and air enters the pore and causes drainage. Equa- tion 23 gives the relationship between the applied moisture tension and the theoretical maximum radius of water-filled pores. By using equation 23 and the volume of soil solution removed under suction, the size and amount of pore space in a soil sample can be determined. Since the pores in soil are irregular in shape and vary in size, the R calculated in equation 23 is a value that is theoretically equivalent to the actual soil pore. McFarlane and Tabor ( 26^^ 265 ) demonstrated the importance of surface tension on adhesion by measuring the adhesion between a glass sphere and a glass plate under saturated conditions. Figure 30

FIGURE 30.—The geometry of a glass sphere adhering to a plate used to compute the force of adhesion. (McFarlane and Tabor, Roy. Soc. London Proc, Ser. A {26J^).)

shows the water film between a flat plate and a sphere at saturation. Since both surfaces in the experiment were glass, the contact angle is the same. At saturation the water film contacts the plate at a circle whose diameter is 4Ä, where R is the radius of the sphere. Following the concept of capillary rise, the force F between the sphere and plate is equal to the perimeter of contact multiplied by the surface tension T^ and the cosine of the angle of contact a. This relation is expressed as F = 4:7rRT cos a. (24) McFarlane and Tabor measured F, the adhesion force, for various radii of beads. They used a clever method where the spherical glass beads were suspended on the end of a fine fiber. The vertical plate and bead were brought into contact; then the plate was moved back until the bead fell away under the action of gravity. Figure 31 shows the forces acting and shows how the angle 0 is a measure of F. Ad- hesions as low as 10"^ grams could be readily measured with the apparatus. Figure 32 shoAvs the results of this work. From the slope of the line and equation 24, the surface tension for water could be calculated. This method resulted in a value of 67.3 dynes per centimeter, whereas the accepted surface tension of water at the same temperature is 72.7 dynes per centimeter. They felt, however, that the value was close enough to demonstrate the importance of surface SOIL DYNAMICS IN TILLAGE AND TRACTION 45

FIGURE 31.—A method used to determine the force of adhesion between a glass bead and a flat plate.

100 r

.02 .04 .06 .08 RADIUS OF BEAD (cm)

FIGURE 32. -Effect of surface tension on adhesion. (McFarlane and Tabor, Roy. Soc. London Proc, Ser. A (264).)

tension on adhesion. The values for surface tension for other liquids in table 3 clearly verify the effect of surface tension on adhesion. Fountaine ( 127 ) demonstrated the effect of moisture tension on adhesion. He reasoned that when a soil is saturated and a continuous water film exists between a plate and soil, tension m the \yater at equilibrium would come to the same value throughout the soil mass. To achieve equal tension most of the water-air menisci will move into channels whose dimensions correspond with the tension governed by the relation expressed in equation 23. Some of the menisci may have to assume "forced" curvatures, since they are unable to reach 46 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

TABLE 3.—Surface tension of liquids as determined from measurements of adhesion of thin films on glass surfaces

Surface tension Type of liquid Calculated from Accepted adhesion value Dynes/cm. Dynes/cm. Water 67.3 72 7 Glycerine 59.0 63 5 Decane 22.4 25 0 Octane 19.9 21 8 SOURCE : McFarlane and Tabor ( 26Jf ).

channels of appropriate size. In this manner the water link will give an adhesive strength per unit area of water film equal to the moisture tension. If the plate is pulled from the soil slowly, the water will move through the soil to the water film at the joint. When the force exceeds the moisture tension value, failure occurs. Fountaine ( 127 ) devised the apparatus shown in figure 33 to

SINTERED GLASS BRASS SOIL- PLATE WATER SOIL- ^SOIL SCRAPED AWAY

COTTON- (B) WOOL

WEIGHT

FIGURE 33.—^An apparatus to measure the normal force between soil and a metal plate. (Fountaine, Jour. Soil Sei. {121),) measure the effect of moisture tension on adhesión. Up to 1 week was required for equilibrium, and the load had to be applied very slowly after equilibrium was reached. Rapid loading resulted in higher measured adhesion than calculated. Fountaine reasoned that the high values resulted from increased tension in the vicinity of the film and that the increase was not transmitted through the soil to the sintered glass plate where the exact value of tension was known. Figure 34 shows the results for three soils. The lack of agreement at higher moisture tensions in sandy loam and sand soils was be- ¡SOIL DYNAMICS IN TILLAGE AND TRACTION 47

CLAY LOAM SANDY LOAM SAND

8 12 16 20 4 8 12 16 20 4 8 12 16 20 MOISTURE TENSION (cm) (A) (B) (C)

FIGURE 34.—Effectiveness of soil moisture suction on adhesion for three soils. (Fountaine, Jour. Soil Sei. { 127 ).) lieved due to formation of discontinuities in the water film so that the area in contact with the plate was not known. Attempts to evaluate the exact area by using a low-powered binocular microscope through a glass plate failed. Observations did confirm that bubbles appeared at higher tensions. While no mechanism for explaining the effect of moisture tension on adhesion was presented, the data demonstrated that moisture tension did affect adhesion. With the establishment of surface tension and moisture tension as the primary means for transmitting force through moisture, the factors that affect adhesion can be discussed." Since the wettability of a material affects the angle of contact, factors that influence moisture tension, such as surface tension and wettability, will have direct influence on adhesion. The surface tension of several liquids is shown in table 3. The magnitude of surface tension for soil solutions has been determined for several soils by Kummer and Nichols ( £35 ). Table 4 lists the

TABLE-4.—Surface tension of soil solutions of several soils

Sou type Surface tension Dynes/cm. Cecil clay 72.2 Greenville sandv loam 73.2 Sumnter clav _ 72.7 Lufkin clay _ - _ 70.5 values. Whether the reported values are representative of other soils is open to speculation since these values appear to be the only ones that have been published. Organic compounds such as benzene tend to lower surface tension, but they are not generall}^ found in soil. Salts appear to have little effect on surface tension since they ionize and spread throughout the solution. Increases in temperature decrease the surface tension of a liquid in accordance with the relation 48 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE T ^ To (\-t/UY, (25) where To = the surface tension depending upon critical constants of the liquid, tc = the critical temperature, n = a universal constant, T = the surface tension at any temperature t. Data are virtually unavailable on the importance of temperature on soil adhesion ( S12 ). According to equation 25, however, the natural heating, due to friction, of tillage tools operating in soil should tend to reduce adhesion. Heat has been applied to j)lows in an effort to decrease adhesion and improve scouring. No significant decrease was observed (23 ) but the experiment was not well controlled. Wettability is a measure of the degree to which water will adhere to the surface of a material. A material that is highly wettable will be completely covered with a thin layer of water, whereas a non- wettable material will merely support the water in a large drop on the surface. The angle of contact a, illustrated in figure 35, is a

FIGURE 35.—The wetting angle of a film, indicated by the spreading that occurs, is a measure of wettability. measure of wettability. The greater the angle a, the less spreading or wetting of the material. The angle a is the same angle considered in equation 20 and is a function of both the soil and the solid material. For adhesion to occur, the water must be attracted to both the soil and the solid material. Little research has been conducted on wettability of soils. Jamison ( 191 ) reported soils that were nearly completely resistant to wetting. These soils became coated with waxy materials to the extent that they were waterproofed and absorbed water very slowly. These soils are not typical, however. Kummer and Nichols ( 235 ) determined the wettability of metals that have been used in tillage tools. Soil solutions were extracted from several soils by a laboratory method in which the soil solution was displaced by another fluid. Two specially ground and cleaned plates of test materials were alined parallel and vertical and dipped into the solution. The solutions rose between the plates in accordance with equation 20, and the angle a could be determined from equilibrium heights and distance between the plates as follows: Let œ be the difference in height oí capillary rise between two plates when separated at two distances, Wi and W2. Then from the geometry of the system and equation 20

Al = Ä2 + a?, (26) and 2T cos a 2T cos a 1 = -^ ; /l2à2 =- ————. (27) ~ g p W2 SOIL DYNAMICS IN TILLAGE AND TRACTION 49 Substituting for Äi and Ä2 and solving for cos a gives xgp / WxW2 \ cos a = -^ (28) \Wi - W2J' the equation from which the angle of wetting a can be determined. The experiments indicated that the wettability of different materials by different soils is relatively constant (table 5).

TABLE 5.—Wetting angle of various soil solutions on several types of metal surfaces

Soil from which solution was extracted Type of metal Sump ter CecU Greenville Lufkin clay clay sandy loam clay Degrees Degrees Degrees Degrees Cast iron 65.5 76.7 73.7 66.5 Stainless steel 81.5 80.7 81.8 80.9 Plow steel 76.5 78.5 77.6 75.6 SOURCE : Kummer and Nichols ( 2S5 ).

Several other factors influence adhesion, but their effect has not been clearly demonstrated for soils. The angle of wetting is probably affected by the surface roughness of the material. Presumably, small irregularities act like small capillaries in which water can rise and thereby increase the film contact. The viscosity of a fluid may also affect adhesion, since it will influence the movement of water. Where relatively short loading times are involved, lack of movement may affect moisture tension or the area of contact in the immediate neighborhood of the adhering moisture films. The effect of these factors has yet to be determined for soils. As was indicated in the discussion of friction, several factors affect the coefficient of friction defined by equation 19. Obviously, one factor is adhesion ; furthermore, the effects of adhesion cannot be simply separated from friction. The problem is usually circumvented by specifying equation 19 as the apparent coefficient of friction. That force normal to the sliding surfaces which is due to adhesion is interpreted in a change in the coefficient />t. Since experimentally the apparent coefficient rather than the true coefficient of friction is measured, the apparent coefficient of friction is normally utilized. Haines ( 169 ) demonstrated the importance of adhesion on the sliding friction of metals on soil. The relation is expressed in the form ^' = ^ - tan 8, (29)

where /x' = coefficient of sliding friction, F = force to cause sliding, N = normal force on sliding surface, Ô = angle of soil-metal friction. Haines measured the force required to pull a slider over different soils having a wide range of moisture contents. He calculated the ap- 50 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE parent coefficient of sliding friction /¿^; typical results are shown in figure 36. These data have been duplicated by other workers.

500

10 20 30 MOISTURE (PER CENT)

FIGURE 36.—Effect of the moisture content of soil on the coefficient of soil- metal friction in sand (solid dots) and clay (circles). (Haines, Jour. Agr. Sei., Cambridge University Press ( 169 ).)

In general, the curves can be explained on the basis of adhesion. In sand, the initial flat part of the curve corresponds to the true coefficient of sliding friction, as considered in equation 19. As water is added, moisture films develop between the slider and the soil, and adhesion increases. The increase in adhesive force acts in the same way as an increase in the weight of the slider, so that the increased frictional force may not be due to a change in ¡JL- with moisture but rather is due to an apparent change in the normal load caused by adhesion. Since Haines had no measure of the increased adhesive force and hence the increased normal load, he calculated an apparent coefficient of sliding friction /JL% as defined by equation 29. Fountaine and Payne ( 127, 331 ) conclusively proved that adhesion acts as an increase in normal load under saturated conditions. They used the experimental setup illustrated in figure 37. The normal load on the slider could be applied either by moisture tension or by weights. A series of different normal loads was applied to the slider by each method, and the friction angle was determined from observations of four soils. The results are given in table 6. Since the friction angles were similar and since the curves of normal load versus friction force would pass very close to the origin, the authors concluded that adhesion acts as a normal load and is, in fact, equivalent to normal loads applied by weight in low-moisture-tension ranges. The equivalency at higher moisture tensions is open to speculation ; no work has clearly demonstrated the effect one way or the other. Since the range covered in the experiment represents the range where the apparent friction angle is high, the effect must be considered; and it helps explain soil-metal friction. SOIL DYNAMICS IN TILLAGE AND TRACTION 51

WEIGHT APPLIED HERE IF REQUIRED-I

SOIL CYLINDRICAL SINTERED GLASS CONTAINER

FARADAYS WAX

MOISTURE TENSION

LOADING BUCKET-

FIGURE 37.—An experimental method used to control soil moisture suction on a sliding surface. (Payne and Fountaine, Nati. Inst. Agr. Engm. {331),)

TABLE ß,—Effect of loads applied hy mechanical weights and hy soil moisture suction on the frictional properties of several soils

Angle of sliding friction Soil type Normal load applied Normal load applied by mechanical weights by moisture suction Degrees Degrees r^lp-iT InfiTTi — ——— 35 41 26 TJOPTTI — — — — — 27 Snnrlv lofiTTi 27 31 17 Sand 16 SOURCE : Payne and Fountaine {331 ).

Nichols {316) has classified the general phases of soil friction. The phases are largely determined by the moisture content of the soil (fig 38). Moisture content is related to the area of moisture ñlm present and to moisture tension; moisture content can thus be used to explain the general behavior of soil-metal friction. According to Nichols' classification, the friction phase is found when the soil is dry. As moisture is added, adhesion.begins and the apparent coefficient of friction increases. The adhesive phase is found when enough water is present to cause high adhesion but not enough to provide a free water surface. 52 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

0.7 - 1 0.6 - /

0.5 - / 0.4 ^,x^ 0.3 FRICTION ADHESION LUBRICATION 0.2 PHASE PHASE PHASE 0.1

1 L_i 1 10 15 20 MOISTURE CONTENT (7o)

FIGURE 38.—General phases of soil friction used to identify soil reactions at different moisture contents. (Nichols, Agr. Engin. (5i6).)

The rapid increase in apparent coefficient of friction in the adhesive range can be explained from adhesion. As the moisture content increases, moisture tension decreases and adhesion decreases as shown in figure 34. But since the normal load is a function of total contact area, presumably the area is increasing faster than adhesion is decreasing. The increased normal load thus gives a higher apparent coefficient of friction. As more moisture is added and moisture tension becomes even less, presumably a situation is reached where adhesion decreases more rapidly than the area of moisture film increases so that an actual decrease in total load results. The final lubricating phase occurs when enough moisture is present to cause low moisture tension and a free water surface to "lubricate" the soil-metal surface, and thus reduce total adhesion. Lubrication was perhaps a poor choice of words since data indicate that the apparent coefficient of friction is usually higher in the lubrication phase than in the friction phase. 2.9.4 Abrasion When a large amount of soil slides over the surface of a machine such as a metal tillage tool and the frictional forces are high, abrasion may make the machine ineffective. Parameters of both the tool and the soil are important in abrasion (4^, 30), The abrasion properties of soil are similar to the dynamic frictional properties. When the soil acts as a rigid body, rolling of the soil grains is prevented; and scratching, breaking, or grinding of the machine surfaces may be excessive. The same principle applies to metal in which hard carbide crystals are held in a firm matrix. The hardness (relative to that of the sliding material), sharpness, size, and amount of soil grains and the SOIL DYNAMICS IN TILLAGE AND TRACTION 53 water content of the soil mass are physical characteristics or conditions that affect abrasion. The metal characteristics that affect abrasion are hardness, strength, and toughness. Dynamic parameters of an abrading system include the stresses on the sliding surface and the duration, and rate of sliding so far as it influences the temperature and stability of the sliding surface. Abrasion as a dynamic property of soil is particularly manifest when its influence is permitted to accumulate on a sliding surface. Wear of the soil by abrasion is neither desirable nor of consequence so its effect is disregarded. Wear of machine surfaces, on the other hand, has had practical effects ; studies have therefore been directed toward securing remedial actions. The mechanics of failure during abrasion is difficult to study because soil does not act as a rigid body system. Stresses are complex and a number of parameters in the soil-machine system have not been fully characterized and evaluated. 2.10 Dynamic Versus Static Properties The concept of dynamic and static properties of soil has been used in this chapter. A dynamic property comes into play in the response of soil to applied forces. The response usually results in movement that can be considered as rigid body movement or as internal movement in terms of stress and strain. A dynamic property, however, does not have to change in size during movement. Conversely, the size of a static property does not have to remain static during movement. The connotation of the definition implied is the response of soil to applied forces and not the size of the property. Thus, macro- pore space is classified as a static property even though its size probably will change as the result of applied forces. Static is assigned as a definition because the property exists even when forces are not applied. On the other hand, friction as a physical force in tillage or traction does not exist until the soil responds to a force and tends to move. After motion begins, the size of friction may or may not be static. The concept of static and dynamic properties must be clearly understood if it is to be profitably used. Separating properties of soil into static and dynamic categories is one means of characterizing soil. Characterizing soil with regard to plant growth, tillage tool design, or road building so that desired results can be obtained has been and still is one of the goals of researchers. One difficulty is that each area of interest probably requires a different system or means of characterizing soil. Defining dynamic properties in the foregoing manner provides a method to systematically develop a characterization that will apply to the reaction of soil to applied forces. Such a procedure, however, does have limitations. If parameters of equations describing soil behavior are the properties that form the basis of a characterization, then the equations must relate to fundamental factors of interest. If not, the characterization will be un- duly complex, will probably lack physical significance, and may have very limited value. Such possibilities result because the equations must be developed from simple experiments and the conclusions extrapolated to the more general conditions found in nature. Unfortunately, many relations can appear to be important under 54 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the controlled conditions of a simple experiment when, in reality, a more fundamental principle is involved. For example, Newton was aware that material bodies fell to the ground according to Galileo's laws of falling bodies, that all projectiles followed parabolic paths, and that the planets moved around the sun in elliptical orbits according to Kepler's laws of motion. The equations for each phenomenon were complete and accurate. Yet Newton showed that each phenomenon was in reality part of a more fundamental behavior, which he represented in one simple equation that is the basis of his classical theory of gravitation. From his one simple equation, all the other equations can be deduced and the physical significance is much easier to understand and explain. Such a possibility can occur with soils. Furthermore, simple experiments can inadvertently control a factor of which the researcher is unaware so that erroneous conclusions are made. Eesearchers using parameters of equations to characterize soil must strive to relate fundamental and independent quantities that have been observed over as wide a range as possible. Only in this manner can a simple yet representative characterization be developed. ASSESSMENT OF THE DYNAMIC PROPERTIES OF SOIL

3.1 Soil as a Physical System Soil is a granular medium that varies in composition from organic peat to gravel and that may contain various amounts of water. The soil physical system is continually being subjected to external forces and is, therefore, dynamic. These external forces may be environmental (climate, plants, animals, and micro-organisms) or mechanical (forces applied by man using some type of machine). The specific reaction of the soil to these forces is of interest. The forces provide the means for changing soil from one condition into another and the reaction indicates the kind and degree of change. If one is to be able either to maintain a soil condition or to change it to a more suitable condition, he must first have an understanding of soil behavior ; this behavior must eventually be properly described. Soil conditions and properties, widely varying types of forces, and widely varying types of behavior must all be included in any description before the descripjtion can be satisfactory. The obvious complexity of such a description requires that broad but realistic classifications of reactions and soil conditions must be made. The concept of dynamic properties presented in chapter 2 is an attempt to make such a classification. The first broad classification to consider in simplifying a description of behavior is the reaction of the soil to an applied force system. If the forces cause the soil to yield, the reaction of the soil may be active ; if the soil can support the forces, the reaction may be passive. To illustrate, consider the following situations. When a soil is subjected to a dominant force system such as the force applied by a plow, the reaction of the soil is active and movement of the soil is determined largely by the geometry and method of operation of the plow. On the other hand, if the soil is subjected to a transmitted force system such as a low-velocity gas stream, the soil resists the force and the gas flow through the soil is controlled primarily by the geometry and size of the soil pores. Here the reaction of the soil is passive. Thus, depending on the role of the soil, either its dynamic or its static properties become operative to an applied force system. Static and dynamic properties of a soil mass that are operative in soil behavior are not necessarily the same as those of the soil material. The concept of a static, dynamic, or material property uses the meaning of property in its broadest sense, namely, a characteristic quality or trait proper to a person or thing. With this broad concept, properties themselves can and should be categorized according to purpose or intent. 55 56 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE One logical category identifies physical properties of the material. For example, a piece of metallic wire can be identified by specifying its chemical composition, size and shape, crystalline structure, and density. These properties can be identified and measured without regard to any functional use of the wire. If, however, we wish to describe what happens to current when a voltage is applied to the wire, we must describe the passive reaction or behavior of the wire and the dynamic action of the current. From experience we know that an electric current ñows in accordance with Ohm's law and the electrical resistance of the wire is the property associated with the electrical conductance behavior. Even though the particular piece of wire can be identified by its physical properties, the relation of these properties to the electrical resistance is neither obvious nor easily determined. Thus, an electrical behavior property—that is, resistance—is not the same as a physical property. It is a different kind of property that characterizes the wire with regard to dynamic action of the current under the influence of the applied voltage. The same wire could be used to support a weight, and a different behavior becomes of interest. How does the wire react to an applied force ? Experience tells us that the strength of the wire is important in the dynamic action ; therefore, strength is another kind of behavior property. The wire stretches, and Hook's law may be used as a simple mathematical expression to describe the reaction. The essential difference between physical properties and resistance and strength properties centers on the characterization being attempted. Physical properties attempt to characterize the material in question and no specific use of the material is implied. Eesistance and strength properties characterize the reaction of the material in a specific situation where some use for the material is implied. These properties may properly be called behavior properties. While characterization of behavior also involves identification, the main emphasis is on the implied use and characterization of the action of the material. Identification properties and behavior properties are, therefore, two broad, convenient classifications of properties. The static and dynamic properties of interest in the examples of the plow and low-velocity gas stream are behavior properties rather than physical properties. Dynamic behavior properties of the soil became involved when the plow applied forces to the soil and the soil yielded. When the low-velocity gas stream was applied, the soil resisted and static behavior properties of the soil became involved. Simultaneously, however, d3^namic behavior properties of the gas were involved. The active physical reaction of the soil to the plow must be described by a soil-machine mechanics, whereas the passive physical reaction of the soil, which guides and confines the flow of the gas, must be described by passive behavior properties. The dynamic action of the gas, on the other hand, must be described by fluid mechanics. Static and dynamic properties are thus behavior properties that characterize the reaction of the soil to applied forces. As a general rule, areas in which reaction of the soil is passive are considered in soil physics. The behavior capacity and the transmission characteristics of the soil with reference to the movement of air, water, and heat have been of particular interest ( 5, 32. 2H. 877 ). SOIL DYNAMICS IN TILLAGE AND TRACTION 57 Active and passive reactions must be recognized as separate if behavior is to be fully understood and described. Nothing precludes these two reactions from going on simultaneously. The dynamic reaction affects the condition of the soil. The condition of the soil, in turn, affects the size of the passive properties. An example of a simultaneous action might be wetting that causes soil swelling which, in turn, changes porosity and, consequently, the conduction of w^ater and air. As was discussed in section 2.10, the size of a dynamic property does not necessarily change during soil movement and, conversely, the size of a static property does not necessarily remain fixed. The distinction is on the action of the soil in any situation. Figure 39 provides a schematic illustration of soil behavior in which passive and dynamic behavior properties of the soil are brought into play by dominant or transmitted force systems. The complexity of describing the reaction of soil to any applied force system can only be partly envisioned from the oversimplified schematic relation shown in figure 39. Generally, man's purpose or use for soil has been more directly related to the static properties of the soil that describe its in situ condition. For example, plant growth is known to be affected by porosity, which controls moisture and air movement. Soil temperature also affects plant growth, so that heat capacity and rate of heat exchange are of interest. The pressing need to improve and increase the capacity of the soil for utilitarian purposes has spotlighted the apparent static properties. Much emphasis has been directed toward a study of passive soil behavior in now phenomena. The need to improve relations of this type has been so obvious that attempts have also been made to relate soil conditions to behavior results in situations where dynamic properties were involved. For instance, trafficability of soil has been expressed in terms of static soil conditions ; yet the very action oiP obtaining traction involves an active, not a passive, reaction to soil. Similarily, the stability of building foundations and soil impedance to plant root development involve active rather than passive soil reactions. As figure 39 indicates, however, soil conditions characterized by static properties are affected by any active reaction. Eelating behavior directly to static properties when active reactions of the soil are involved thus must be a complex task and perhaps even a futile one. Even when soil reactions are passive, behavior is complex. This passive behavior involves the movement of materials other than the soil, but the movement is governed or modified by static soil behavior properties. An equation to describe soil behavior will require some form of force input to the soil. This input, together with the modifying inñuences of the behavior properties, causes the output of the equation—that is, the reaction in terms of air or water movement. Thus, the static properties support the dynamic action of the transmitted force system. Figure 39 shows that not only the dynamic inputs (forces) but also the static property that characterizes the specific behavior of the soil must be known and described. The input of the metallic wire, discussed earlier, could be adequately described in terms of voltage. With soil behavior, however, the forces applied to the soil by climate, plants, animals, and soil micro-organisms 58 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

■■¡■1 ^BíéíU^^^^^^V FORCE SYSTEM Static State Properties • Position • Structure • Density Tillage, Climate - Properties Behavior Capacity Properties • Distribution • Active - - Strength • Direction • Passive - - Transmission • Magnitude Material Properties 1 • Time Dependence • Texture • Minerals • Chemical Composition r I T

SOIL YIELDS OR MOVES a r SOIL RESISTS MOVEMENT

DOMINATING FORCES TRANSMITTABLE FORCES

Dynamic Behavior Properties Passive Behavior Properties • Cohesion • Pore Radius ^ Friction • Tortuosity of Pores # Adhesion • Thermal Characteristics

ALTERED SOIL TRANSMISSION ACTIVITIES Static State Properties • Position Behavior • Structure • Density # Aeration Behavior Capacity Properties # Water Movement • Active Strength # Heat Exchange • Passive - Transmission

DOMIMANt FORCE SYSTEM TRANSMITTED FORCE SYSTEM L • MIXED FORCE SYSTEM • J FIGURE 39.—Relation of static and dynamic behavior as a means of characterizing soil reaction to an applied force system. are so ill defined and involved that their magnitude and form are generally not known. Thus, describing behavior in quantitative terms, even for passive reactions, becomes almost impossible until the forces can be adequately described. At any one instant in time, forces such as those from climate can cause a passive reaction; water entering soil is an example. When the water content of a soil increases, these same forces can simultaneously cause an active reaction such as swelling. Thus, soil con- SOIL DYNAMICS IN TILLAGE AND TRACTION 59 ditions are often not static with respect to time but do, in fact, change with time since the forces change with time. The actual condition of the soil at any one time is, therefore, a function of the past history of forces. Since this history is generally not know^n, the condition is attributed to such vague unknown quantities as weathering, microbial activity, crop rotations, and aging. The inability to define forces and the time dependence of forces are two factors that greatly complicate describing behavior. Mechanical forces such as those usually applied to a soil by tillage tools or traction devices can be more specifically described than can climatic or biological forces. Furthermore, their action is of relatively short duration and their magnitude can be controlled. Con- sequently, mechanical forces as a group can be separated and studied with relative ease. It is this isolated group that is considered in detail in this handbook on soil dynamics. Since mechanical forces that are universally dominant forces cause soil reactions, behavior properties rather than static properties describe the reaction. Dominant forces cause the soil to yield and become active rather than passive in the soil reaction. A detailed study of behavior resulting from mechanical forces, therefore, requires a detailed study of dynamic properties. To describe behavior in some rigorous manner, both input (forces) and behavior (the soil's reaction) must be considered. The forces cause the action, whereas the reaction determines the kind and amount of change in soil condition. The action and the reaction are equally important and must be properly described. The inñuence of the condition of the soil on the reaction must also be indicated. Behavior properties provide a logical means for describing this influence. A relation is, therefore, implied to exist between physical and behavior properties. A unique relation must exist because once a finite amount of material is isolated for subjection to a force system, its physical properties along with its behavior properties are fixed and determined. If these properties change during the action, the change can theoretically be included in the description of behavior. A unique though possibly complex relation, therefore, must exist between physical properties and each behavior property. The relation between physical properties and behavior properties can be more clearly seen when two facts are recognized. First, physical properties primarily identify soil and its condition. They are always in evidence. Behavior properties are made manifest only when a specific action occurs. An action is not necessary for physical properties to exist ; they are fundamental entities in themselves. A behavior property is not fundamental in itself ; rather, the specific action is the fundamental entity and its defines the behavior. The second fact is that static state and material properties (physical properties) are independent of each other. A soil may be found either in a dense state or in a loose, pulverized state. The soil material is the same but its state is different. In a similar manner, different soil materials can exist in the same static state. Therefore, properties that identify a soil material and properties that identify its static state are, within reasonable limits, independent of each other. Furthermore, since physical properties describe the nature 60 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE of a material and its nature determines how the material will behave, behavior properties must be a function of physical properties. In other words, in a mathematical equation that describes a relation, state and material properties are independent variables and behavior properties are dependent variables. Researchers have intuitively reasoned that a unique relation must exist betwêen physical properties and behavior. If such a relation does not exist, a different behavior would result whenever the same system of forces is applied in the same manner to a material in a given condition. Repetitive behavior, however, is observed when carefully controlled and standardized procedures are followed. Knowledge that such relations exist has often guided research efforts in wrong directions. To illustrate, again consider the metallic wire and Ohm's law. Available knowledge indicates that the resistance of a piece of wire is inñuenced by the length of the wire, cross- sectional area, chemical composition, and temperature. All these are physical properties that identify the piece of wire. Imagine the difficulty of describing behavior when voltage is applied if these physical properties were to be included in the description without knowledge of the behavior property, electrical resistance. Once resistance has been identified, however, a logical means for describing the behavior of current flow exists. First, behavior is described and a behavior property is identified (Ohm's law and resistance). Then the behavior property rather than the behavior itself can be studied. Recognizing the existence of behavior properties and first search- ing for them is a means of simplifying the problem of describing behavior. The possibility exists that one physical property or some simple combination of two or three physical properties might be directly equivalent to a behavior property. In such instances, the relation between physical properties and behavior may be found without first identifying a behavior property. When the complex behaviors of soil are observed, the possibility of directly relating physical properties and behavior seems remote. It looul'd thus appear that the ^ relationship hetween the physical properties that intuitively must affect dynamic properties and hence soil hehavior must await means of identifying and quantitatively measuring the dynamic properties. To fail to recognize this can only lead to confusion and frustration. 3.2 Dynamic Parameters In the preceding section, dynamic properties were shown to be capable of characterizing soil as it reacts to applied forces. Inter- relations betwêen applied forces, dynamic properties, and behavior are implied in figure 39. The figure also suggests the qualitative nature of these relations. The soil and the applied forces are both of importance so that once a specific soil is isolated and a specific system of forces applied, the resulting behavior is determined. The behavior must be considered in a restricted form; hence, a statistical form of result is not produced. The soil and forces thus are primary and basic, and the behavior is derived from these basic factors. The forces, howêver, are the prime movers of any action. They cause the action, so they may be properly termed inputs to any equation that expresses the manner of soil behavior. These inputs act son. DYNAMICS IN TILLAGE AND TRACTION 61 on the soil, which may be schematically represented as a black box that always correctly simulates soil behavior. The output from the box is the result of the action. Thus, the forces, the black box, and the results are related; and a description of the overall relation suggests a function that can be expressed by a mathematical equation. The equation should relate inputs to outputs through the black box so that the equation, in effect, describes the behavior under consideration. In reality, the equation defines the dynamic behavior properties. The relations implied in figure 39 suggest that each dynamic property may appropriately be defined by a mathematical equation. Distinguishing between an initial identification and a subsequent qualitative definition of dynamic properties is necessary in order to clearly understand the relations between dynamic properties and behavior. Consider the possible evolution of a hypothetical dynamic property. By some means (probably experience) a specific behavior is noted to be repetitive and of importance and, as a result, behavior is isolated and observed. Once the behavior has been isolated, a dynamic property should be identifiable to characterize the soil's contribution to the behavior. Since a dynamic property is a behavior property, it must be qualitatively defined by an equation as previously outlined. Thus, the second step in the evolution of a dynamic property is its qualitative definition by an appropriate equation. Determining such an equation requires much more knowledge than does the identification of a dynamic property. Indeed, several isolated behaviors that have been observed in soil were discussed in chapter 2. Only a few, however, were qualitatively defined by accurate equations. The gap between identification and qualitative definition of dynamic properties may be very large and difficult to span. A qualitative definition of a dynamic property is useful because the equation that identifies it also identifies the inputs and outputs of the soil behavior. Also, the equation generally indicates the trends in the behavior. A quantitative description of behavior is required before one can predict and control behavior. A quantitative description requires a third step in the evolution of a dynamic property—the establishment of a unique correspondence between the magnitudes of inputs and outputs of the basic equation. Such a correspondence requires that the inputs and outputs be adequately described so that they can be represented numerically. Furthermore, the dynamic property must also be represented numerically to characterize the soil's contribution to the behavior. Dynamic parameters provide a means for numerically representing dynamic properties. The parameter is defined as a quantity or constant whose value varies with the soil conditions or circumstances. Each equation that defines a dynamic property contains one or more mathematical parameters that are measures of the dynamic property. Thus, for a given circumstance (soil in a specific condition), the numerical value of the parameter is a constant; but, as the soil condition varies because of such things as a change in moisture content, the numerical value of the parameter may also vary. In other words, the dynamic parameters are precisely determined by the physical 62 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE properties of the soil although the exact relation may not be known. A complete quantitative description of behavior of the soil to forces can be determined after one has identified, qualitatively defined, and finally quantitatively assessed dynamic parameters of soil. Although not indicated at the time, the requirements for a quantitative description of behavior were met when dynamic properties were discussed in chapter 2. For example, when soil deforms, the output of the behavior equation is the resulting movement. Strain was discussed in section 2.3 as a means of describing movement so that numbers could be assigned. The forces acting in the system cause the strain ; and stress, which numerically describes the forces, is the input. Stress-strain equations replace the black box and define a dynamic property, which reflects behavior. The parameters of the stress-strain equations numerically assess the dynamic property. Another example of behavior is shear; the output differs in this instance, since the output description itself does not need to be quantized. As indicated in section 2.8.1, shear is a yield condition; and the output is the failure itself. Although the failure is clearly described, a number is not necessarily specified. The input for shear is again the applied forces, and they are the forces acting at incipient failure. The relation between the stresses at incipient failure and yield provides the real mathematical function of the black box. Thus, equation 18 defines the dynamic property shear, whereas cohesion and the angle of friction are the dynamic parameters that numerically represent shear. Both stress-strain equations and shear yield equations are examples of force inputs that are related to behavior outputs by an equation that represents the behavior. A superficial inspection of the previous analysis may raise the question of whether forces are always inputs. In shear, for example, shearing stress may seem to be an"^ output of the behavior since the shear stress is the maximum value that can be obtained for the situations under consideration. If the intended purpose of the soil is to obtain traction, shear stress may be visualized as the limiting value of traction for the particular situation ; hence, shear stress is of direct interest and appears to be an output of the behavior. Shear stress, however, causes the failure; failure does not cause the shear stress. The confusion is explained by Newton's Third Law of Motion, which states that every force has an opposite and equal reaction force. Thus, the shear stress has an opposite reactive stress, and this reactive stress is the limiting value when the intended use of the soil is for traction. Behavior and intended use of the soil, therefore, must be kept separate if the mechanisms in behavior are to be clearly understood. Dynamic parameters are not always present in equations defining dynamic properties. Such a situation arises when the behavior output is not ¡quantized and the force input is simply represented. In fact, the situation can be so simple that no equation is required. In tensile failure, for example, the magnitude of the normal stress completely describes the behavior at failure. Dynamic parameters, thus, are not basic because they are defined only by the equations that represent the mathematical models of the behavior. It is the behavior and implied dynamic property that are real and basic. For SOIL DYNAMICS TN TILLAGE AND TRACTION 63 example, soil-metal friction is real and unique, and equation 29 defines the dynamic property. Only one parameter is needed to represent the property ; however, we might choose some other model to represent the property so that a different mathematical parameter or even more than one parameter might represent the same property. Dynamic parameters, therefore, are useful but are onl}^ a means for numerically representing the basic factor, the dynamic property. Assessing dynamic properties involves assigning numbers to dynamic parameters. Since the relations between the parameters and physical properties are not known, some means of measuring the parameters is required. Dynamic parameters can be extremely useful even without knowledge of their relation to physical properties, if the parameters can be assessed. In metals, for example, specifying the yield strength permits a quantitative design of some specific use for the metal such as an element of some machine or building. Yet metallurgy, which deals with physical properties of metals, cannot always provide the quantitative relationship between the physical properties and yield strength. While these relationships are highly desirable, the lack of relationships between physical properties of soil and dynamic parameters of soil does not negate the usefulness of the parameters. As indicated in chapter 2, not all dynamic parameters have been identified. Lack of suitable stress-strain equations is an example. Even further, some that have been identified are not readily assessed. Indeed^ this is the crux of the soil dynamics dilemma. If all the idealized dynamic parameters could le successfully measured,^ considerable progress could le made in developing a quantitative description of behavior. With such descriî)tions, relations between soil and machines could be developed, a rigid mathematical soil-machme mechanics could be established, and the soil's capacity could be better used for a utilitarian purpose. Practical considerations, however, dictate that relations between soil and machines must be established even if an empirical approach has to be followed. Consider- able research, therefore, has been directed toward correlating machine performance with one or more dynamic parameters of the soil. Thus, in both theoretical and empirical approaches, dynamic parameters must be measured—that is, their identity and magnitude must be defined and assessed. Before techniques for measuring dynamic parameters are discussed, composite parameters should be defined. The parameters indicated in chapter 2 may all be classed as independent parameters because they appear in the mathematical models as independent parameters that identify and assess the magnitude of the single property under consideration. A composite parameter, however, can also be visualized. For example, the bearing strength of soil is useful for designing footings. Such a mathematical model conceives of the unit pressure that the soil will support as a measure of the soil's capacity to support a load. Obviously, this unit pressure is a yield condition and can possibly be described in terms of cohesion and internal friction. Thus, bearing strength could be a composite parameter of cohesion 64 AGRICULTURE HANDBOOK 31G, U.S. DEPT. OF AGRICULTURE and internal friction. A composite parameter, therefore, is not independent since it combines the effects of two or more factors that are known to be independent. From its mathematical model, however, the composite parameter may appear to be independent. The bearing strength parameter is represented as force divided by the area over which the force acts, and so it appears to be unique and independent. The difference between an independent parameter and a composite parameter is thus one of degree rather than kind. A parameter cannot be classified from its own mathematical model but must be classified on the basis of additional knowledge. For example, at one time matter was tliought to be composed of three particles—electrons, protons, and neutrons.: Each defined an independent unit. Today, many additional particles have been identified so that the earlier three are no longer independent but are themselves composites. Similarly, a dynamic parameter may be classified today as independent but in the future may be found to be composite. Nevertheless, dynamic parameters are a systematic means of identifying and quantizing factors of importance for describing the type of soil behavior under consideration. Their usefulness depends on the accuracy of the defining mathematical equation and the success of measuring the parameters, not on their specific relation to physical properties. Both independent and composite parameters must be measured in both theoretical and empirical approaches for solving soil-machine problems. Composite parameters must be used when independent parameters have not been identified and when measurements are difficult or time consuming. In fact, no feasible means has yet been devised to make some of the desired measurements. The procedure is the same for measuring both independent and composite parameters. Generally, an apparatus is devised that applies and controls either forces or movements, or both, so that the specific quantities of interest can be observed and measured. Thus, a shear box (fig. 27) can be used to control the surface of failure in the soil and the normal force N while the force F causing failure is nieasured. Manipulation of the data permits evaluating the desired parameters. The apparatus thus attempts to simulate the conditions represented by the mathematical model. Too often, however, an apparatus does not exactly duplicate the action represented by the mathematical model so that the apparatus itself influences the results. Measurements in such instances do not yield values that intrinsically characterize the soil but rather values that characterize both the soil and the device. Inaccuracies can result because the mathematical model is wrong or because the apparatus does not represent the model, or both. In other instances, the apparatus may measure in one range of forces while the machine mav operate in another so that the magnitude of the parameters is different. For example, if the coefficient of the soil-metal friction varies with normal load, both the device used to assess the coefficient and the machine to which the coefficient is applied should use comparable normal loads. In spite of these complications, progress has been made in using dynamic parameters to describe soil-machine relations. Some of these SOIL DYNAMICS IN TILLAGE AND TRACTION 65 relations are discussed in later chapters. In this chapter, brief attention is given to the methods and techniques that have been used to assess both independent and composite dynamic parameters. 3.2.1 Measuring Independent Parameters By using appropriate apparatus, specific independent dynamic parameters of shear, tension, compression, plastic flow, friction, and adhesion can be measured under highly controlled conditions. As indicated earlier, the methods that have been developed are not completely accurate or satisfactory. Specific instructions on how these measurements should be made have been described in other publications ( 7, 11, U, 2J^5, £69, 4^j8, 1^50, JiS8). In addition, specialized measurements are described in a number of research papers cited in this handbook in connection with specific topics. Undoubtedly, these measurement techniques will be modified or improved as research is continued; however, techniques for a number of measurements have been standardized to some extent, and an effort should be made to use these when practicable. 3.2.7.7 Shear Shear was interpreted in section 2.8.1 as a failure or yield condition, and the various ramifications were discussed. Basically, failure was adjudged to occur, and the stresses acting at incipient failure were used to describe the condition. A mathematical model representing the relations between the appropriate stresses was envisioned, and the model suggested that shear was represented by two parameters. One of these is a cohesive parameter, which depends upon the strength of in situ bonds. The other is made up of frictional resistance which results from the sliding of soil over soil and which appears to obey the laws of friction. All present measurements of shear attempt to evaluate the two parameters C and (/). Keep in mind, however, that these are parameters of the mathematical model representing shear. Physically, the two parameters are not separate or unique entities and so are not true physical properties. Until a different model is proposed, however, measurement of shear will center around evaluating cohesion and internal friction ( 7, 12), The means most widely used for measuring shear can be appropriately described as a direct shear apparatus. A direct shear apparatus permits one to control the failure surface and simultaneously provides a means for determining the appropriate stresses. Figures 27 and 28 illustrate a method that can be used on disturbed soil samples. An advantage of direct shear methods is that they can be adapted for in situ measurements. The form of the apparatus for in situ measurements is generally as shown in figure 40 and failure is envisioned to occur as in figure 40, B. Figure 40, A illustrates a possible failure that is not represented by the assumed mathematical model describing shear. In this case the displacement of the device and the deformation of the soil are not the same. When this type of failure occurs, conclusions will be incorrect because of the inaccurate representation. Other possible misrepresentations may result from nonhomogeneous stress distributions along the shearing surface. In 66 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE N N

(A) (B)

FIGURE 40.—In situ direct shear apparatus showing shear failure : A, Soft conditions; B, hard conditions.

addition, strain may not be uniform along the failure surface ; therefore, the observed movement of the apparatus does not represent movement at the failure zone. Jenkin ( 200 ) demonstrated the importance of distinguishing between conditions simulating constant volume and those simulating constant stress. In an extreme condition represented by compacted sand, he found that the force required to rotate a steel plate increased 270 times when the volume was not permitted to expand during shear. Confinement caused shear within individual sand grains rather than between grains, hence the increased force. Experiences such as Jenkin's indicate that shear should be measured under controlled stress. Extreme care is required to insure that the envisioned model is being accurately represented by the apparatus. The precautions and techniques will not be covered here. The degree to which an apparatus duplicates conditions represented by the assumed mathematical model depends on the kind of apparatus and the techniques of its use. As a result, different shear values are often obtained on the same soil with different apparatus. Various aspects of their appropriateness will be discussed in conjunction with individual apparatus. In all direct shear apparatus, the normal and tangential forces are measured as well as the relative movement of the apparatus with respect to the soil. The normal and tangential forces divided by the appropriate failure area gives the required stresses. Movement is generally expressed in terms of strain. The data can be represented as shown in figure 41, where the tangential or shearing stress is plotted versus the strain for a constant normal stress. The three characteristic curves represent the range of behavior observed. Condition A,is characteristic of highly cemented and dried soils or hard, clean sands that exhibit a high peak strength. Once initial failure occurs by breaking cemented bonds that reflect high cohesion, the measured stress lessens and the friction component is primarily represented. Condition B represents the other extreme where the soil is loose and has low cohesive strength. Any number of intermediate behaviors such as indicated by condition C may be found. From data such as indicated in figure 41, the parameters of shear can be determined. Incipient failure is adjudged to occur either when the shear stress reaches a definite peak (condition A) or when the shear reaches a plateau (condition B). A series of shear meas- SOIL DYNAMICS IN TILLAGE AND TRACTION 67

STRAIN FIGURE 41.—Typical shear stress-strain relations for soils in three conditions : A, Cemented; B, loose; and C, dense. Each curve is at a constant normal load. urements are made at different normal stresses for a given soil condition. The shear stress at incipient failure is plotted versus the associated normal stress, as shown in figure 42, J., where points

i T B^ ,.^_ rc -a i w

(A) (B)

FIGURE 42.—Typical direct shear data indicating A, the components of shear, used to construct B, the Mohr's circle representing a specific point of failure.

A, B, and C represent experimental points. The experimental points usually lie on a straight line or a smooth curve that can be extrapolated to zero normal stress. The slope of the curve defines the angle of internal friction <^, whereas the intercept of the extrapolated line with the shear stress axis defines G, the cohesion. As discussed in section 2.8.1, a straight line can be represented by equation 18, which has the form r = 0 -{• cr tan <^, (18) where r = shearing stress, (T = normal stress, G = cohesion, (^ = angle of internal friction. bö AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Equation 18 is, therefore, the mathematical model that represents shear failure. The parameters of the equation, C and <^, are the desired measures of shear. Direct shear data can yield more information than just the shear parameters C and 0. Direct shear data basically provide information concerned only with stress at failure. As discussed in section 2.8.1, the failure stress can be considered to act on a plane. Not only is the orientation of the failure plane of interest, but also the magnitude of principal stresses of the stress state causing failure. Since the line determined by points A, B, and C represents failure states, the line must be a failure envelope for the Mohr's circles discussed in section 2.8.1. Any circle just tangent to the line, therefore, must be a failure circle. Constructing line BO perpendicular to the envelope so that BO intersects the abscissa, as shown in figure 42, ¿, locates the center of the Mohr's circle associated with the failure condition at point B. Constructing the appropriate circle then provides the desired information. Thus, while direct shear data provide values oi C and ^ only, additional information can be obtained by using conditions of the Mohr concept. The simplest types of direct shear apparatus are illustrated in figures 27 and 28. Many types are in use, and some may apply normal stresses in excess of 1 ton per square foot to shear rock fragments ( i^ ). Such types of direct shear have been utilized almost entirely as laboratory apparatus. One unique field type of direct shear for in situ measurements was called the soil truss {177). The truss consisted of a parallelogram mechanism, which was designed to apply normal as well as tangential loads to the shear box in the soil. Adjustments of the lengths of the parallelogram permitted the application of different ratios of normal and shearing forces in order to obtain soil failure. Eela- tionships of T versus c could be constructed from the measured data, since the normal load-shearing force ratio was known for any position of the apparatus. Hvorslev, as reported by the Waterways Experiment Station ( 476 ), developed a unique modification of the direct shear apparatus for in situ measurements. In this method a round shear box was rotated instead of being moved in a straight path. The shearing stress was computed by using, the equation s - -B-, (30)

where M = torque to cause shear, r = radius of the plate, and by assuming that the soil was plastic and thus the stress was independent of strain. Fountaine and Payne ( 129 ) developed a portable apparatus to measure shear strength of field soils. A hollow, circular shear box was driven into the soil until the top of the box was in contact with the soil. The soil against the outside of the box was then carefully excavated before shear failure was measured, so only the soil at the SOIL DYN^AMICS IN TILLAGE AND TRACTION 69

TORQUE

SHEAR BOX WEIGHTS

r/m//M//á

FIGURE 43.—A simple field torsion shear apparatus. bottom of the box was sheared (fig. 43). Markers were placed in the soil inside the shear box so that they were visible through little holes in the top of the box (fig. 43). By watching the position of the markers as the soil was sheared, they concluded that the mass of soil in the shear box moved as a unit and that the rate of strain within the sample could be considered uniform. Cohron ( 79 ) has devised a portable torsion shear of this type that records the shear data without elaborate instruments. In an effort to overcome the fact that the outermost elements must move considerably farther than those in the center, a narrow annulus has been used as a shear apparatus ( 1^8, 162, 2J^5, 397 ). Shearing stress is easily calculated for a narrow annulus by using polar coordinates. An elemental area is given by r dB dr, and assuming a constant shear stress S acting on the annulus area, the force on the elemental area is Srdddr, The force acts at a distance r from the center so that the moment at the center of the annulus is S r^ de dr. Integrating over the appropriate area gives the total moment, which has the form

M Sr^ de dr. J^2 Jo Performing the integration gives

M - 3 70 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE and solving for S gives UI S 277 {n^-r2^y (31) where S = shearing stress, M = torque to shear the soil, ri = outride radius of annulus, ^2 = inside radius of annulus. Another rotating circular apparatus (fig. 44) has been proposed

FIGURE 44.—A vane shear apparatus. in the form of a vane shear ( 7 ). Once driven into the soil, rotation causes shear of soil along the surface of the cylinder, which is generated by the vanes. This device may be used at great depths in the soil without excavations. Measurements may be made at succeeding depths without extracting the shear device, so that a rather complete strength profile of natural soil conditions can be obtained. Shear stress may be computed from the equation UI S = 287rr^' (32) when the vanes have a height-to-radius ratio of 4:1. The vane shear provides no means of varying normal load, although Evans and Sherratt ( 113 ) have estimated values of cohesion from vane shear data. A more sophisticated shear device has been developed in the form of a so-called triaxial apparatus (fig. 45). A cylinder of soil is confined in a thin impermeable membrane, which is tightly sealed around two parallel circular platens located at the ends of the soil columns. As long as the membrane is very thin, it has essentially no influence on the stresses within the sample ( Jiiïl ). When the entire system is submerged in a fluid and pressurized from an external source, the soil is subjected to a uniform pressure on all sides that is eq^uivalent to the pressure in the external chamber. Friction and arching may cause small irregularities in stress distribution at SOIL DYNAMICS IN TILLAGE AND TRACTION 71 -AXIAL LOAD

AXIAL CHANGE

PRESSURE

RUBBER MEMBRANE

DIAMETER CHANGE

POROUS PLATE

-H^O PRESSURE Lhl^^VOLUME CHANGE

FIGURE 45.—Triaxial shear apparatus modified to measure diameter strain. the platens, but there will be considerably less friction and arching in this system than in any other known system. Following an initial uniform loading by the hydraulic system, an additional mechanical axial stress can be applied to the soil by means of a rod that extends out of the external pressure chamber. By increasing the axial stress over the lateral stress, shear failure can be caused. Failure occurs either when a clear fracture is evident or when the diameter of the sample is increased. At incipient failure the principal stresses are known, and the results may be plotted in Mohr's diagrams. Values for C and ^ can be determined from the diagrams, as shown m figure 24. While the name of the triaxial device indicates that the stresses can be controlled along three axes, such is not the case because the two lateral stresses are always the same. Nevertheless, the triaxial apparatus provides an excellent means for making shear measurements. The usefulness of basic shear data depends partly on how it is incorporated into a soil-machine mechanics. As isolated values, C and ^ have no practical usefulness other than to characterize soil conditions. Several attempts have been made to extend the usefulness of the basic shear data. Payne ( 329 ) pointed out that much of the time when soil is being moved, the maximum shear stress only partly represents the conditions. He reasoned that large strains in soil would indicate that the magnitude of the shear stress represented by a plateau, as illustrated by condition A in figure 40, is a more reasonable estimate of the acting stress. The value of 0 obtained m 72 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the normal manner, therefore, might be too high. He proposed use of a residual type of ¿7, which is designated Cr. The value Or was derived from the portion of the shear curve represented by the plateau rather than by the maximum shearing stress. Table 7 gives

TABLE 7.—Cohesion {0) and residual cohesion (Or) values for several soils

Type of soil Cohesion (C) Residual cohesion (Or) P.s.i. P.sA. Sandy loam 1.64 1.13 Sandy loam (nonscouring) 2.32 1.30 Clay loam 3.07 1 78 Loose sand .34 30 SOURCE : Payne {829 ),

some values for cohesion and residual cohesion reported by Payne. The residual value Cr thus becomes an additional dynamic parameter that can be secured from basic shear measurements in certain soil conditions. Cohron ( 79 ) has also measured residual cohesion and advocated its use. An even further departure from C and cj) has been proposed when the shear curve is the shape represented by condition B in figure 40. Many surface soils can be represented by such a curve; and this curve can, in turn, be approximated by two straight intersecting lines. One line is horizontal and represents the plateau shearing stress, Avhereas the other straight line represents the slope of the initial portion of the curve. The strain distance at which the two lines intersect was identified as AT, a deformation modulus ( 2^9 ). Low values of K indicate brittleness, whereas higher values indicate deformability. The deformation modulus becomes another possible dynamic parameter, but its interpretation is based on the mathematical model representing the situation (here the two straight lines that approximate the basic curve) rather than any specific physical property of the soil. A more radical departure in evaluating shear was proposed by Bodman and Kubin ( 4

~~APPLY TORQUE~~

~~WAX~~

~~PLASTER CLOD' OF PARIS~~

~~FIGURE 46.—A method for determining shear of individual soil clods. (Foun- taine, Brown, and Payne, Sixth Internatl. Cong. SoU Sei. Soc, 1956 {128).)~~

cemented to jaws with a quick-drying plaster. The clod can be firmly held and twisted without concentrating stresses on the irregular surface. If the clod is coated with wax, the strength is not altered by water in the wet plaster. Torque is applied to the clod until failure occurs (a clean break), and the shearing stress is computed by means of equation 30. A successful application of the results of the technique remains to be made. The limitations and deviations from the various mathematical models apply primarily to direct shear apparatus. A deviation has also been noted in triaxial shear, and considerable effort has been made to correct for the deviation. Triaxial shear has been widely used in work on foundations and dam construction where the subsoil is often saturated with water. Since water is incompressible, the water may support part of the applied stress. This has been demonstrated in so-called quick triaxial tests and slow-drained tests. In the former, stresses are applied in a matter of minutes and the sample is not allowed to drain. In the latter, the sample is allowed to drain and stresses are applied slowly over a period of days so that often more than a week is required to reach failure. Different values for failure are often observed for the respective tests so that the kind of triaxial test is usually specified when applying the results. Attempts 74 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE have been made to represent the situation by introducing the concept of effective stress defined in equation 34. (/ = (j^- cr^, (34) where & — effective stress, cr = applied stress, cTyj — soil water stress. Mohr's circles are constructed from effective stresses to represent shear failure. The concept has been extended to unsaturated soil where soil-water ' stress now becomes soil-water suction or tension. Childs ( 7Ii, ) demonstrated the equivalence of moisture tension and mechanical stress for low moisture-tension values, but recently Mc- Murdie and Day ( 282 ) have demonstrated a discrepancy. To correct for the discrepancy, they proposed a modification by introducing a coefficient k^ as shown in equation 35. or' = cr + ^cr^. (35) In a simple glass bead system, the coefficient ranged from 0.21 to 2.30. Thus, while the concept of effective stress appears to have meaning in a saturated soil, more research is needed to indicate its suitability in unsaturated soil. More attention has been directed toward measuring and using shear parameters to dynamically characterize the soil than has been directed toward any other dynamic property. As the foregoing discussions indicate, completely satisfactory methods are still not available. In the future, more attention will be required both in conceiv- ing mathematical models to represent shear and in determining means of measuring the dynamic parameters defined by the models. 3.2.7.2 lension The tensile strength of soil is conceived to be the force that is required to pull the soil apart. As discussed in section 2.8.3, such a representation involves specifying the tensile stress acting on the failure surface. The mathematical model is thus very simple, and the only parameter required to define failure is tensile stress at incipient failure. Tensile failure is mathematically much easier to represent than is shear failure. In tensile failure, the stress required to cause failure is probably not related to other possible stresses on the failure surface but is assumed to be directly related to the condition of the soil. In shear failure, the shear stress required to cause failure is determined not only by the condition of the soil but also by the normal stress acting on the failure surface. Because of this, the relation between the various stresses must be represented in shear. Thus, the parameters of the equation representing shear, rather than the stress required to cause failure, become measures of the soil condition (dynamic parameters). The directness of the relation between failure stress and the soil condition results in the simple mathematical model of tensile strength. ^ Soils do fail in tension, so tensile strength is a parameter of practical value. The clearest example of a situation in which tensile stress might be operative is shown in figure 98. The unsupported soil extending beyond the edge of the tool is in tension because of SOIL DYNAMICS IN TILLAGE AND TRACTION 75 gravitational forces. In less cohesive soils, the tensile stress developed in the mass of soil would cause failure. Tension in soil was measured as early as 1833 (32), and a number of methods have been developed to measure it. The only method devised primarily to measure tensile strength in situ appears to be that of Sourisseau ( 407 ) ; the principle is shown in figure 47.

~~FIGURE 47.—A field method for measuring tensile strength of soil. ( Sourisseau, Organ, and Rapts, du II Cong. Internatl. de Genie Rural (^07 ).)~~

Perhaps the most widely used means of causing tensile failure in the laboratory has been with a so-called modulus of rupture procedure. Small blocks of soil are formed in the laboratory by some suitable means, and they are represented mathematically as simple beams. Forces applied as shown in figure 48, A bend the beam; this places some of the beam in tension and some of the beam in compression. Simple beam theory gives an equation for the conditions shown in figure 48, A of

~~S = (36)~~

where F = breaking force, L = distance between supports, B = width of beam, D = depth of beam, S — modulus of rupture, which represents the tensile stresses envisioned to cause failure of a rectangular beam. To obtain the simple expression in equation 36, several assumptions were necessary. The two most important assumptions are that strain is proportional to stress (elastic behavior) and that the slope of the stress-strain relation (modulus of elasticity) is equal in tension and compression. Furthermore, the neutral axis in the beam (division between tension and compression stresses) was assumed to be in the center of the beam. If all of the foregoing assumptions are satisfied, the modulus of rupture can be considered 76 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~(A) (B)~~

FIGURE 48.—Methods of applying forces to simple beams to cause tension failure. the tensile stress at the outer edge of the soil beam at failure. Be- cause the assumptions are not satisfied even for ductile metals, the failure stress is designated modulus of rupture. As shown in figure 48, a beam may be loaded in several ways. The arrangement at the left provides maximum bending at the center of the beam whereas that at the right provides a long central test section in which bending is uniform. Carnes {61)^ Eichards ( 364, ) ? and Allison ( 2 ) have utilized the modulus of rupture in the study of soil crusts. Crusts on the surface of the soil can be collected without undue disturbance. This simple measurement can be used to evaluate their strength in a relatively undisturbed condition. This method has been widely accepted and may be considered as standard {US). Another method of causing tensile failure has been used by Kirk- ham, DeBoot, and De Leenheer ( 218 ) for soil core samples. In this method, a cylindrical sample is compressed laterally until a tensile failure results, as shown in figure 49. The failure stress of the soil

~~FIGURE 49.—The indirect tension method for causing tensile failure, (Kirk- ham, DeBoot, and De Leenheer, Soil Sei. ( 218 ).) is determined from the equation~~

S (37) TTDÚ where F — breaking force, L = length of the sample, D = diameter of sample, S = modulus of rupture. SOIL DYNAMICS IN TILLAGE AND TRACTION 77 The cores must be homogeneous for this method to be reliable. Its utility lies in the fact that core samples provide relatively undisturbed soil samples for evaluation. Mitchell ( 301 ) evaluated this indirect tension-measurmg method for samples of concrete, and he concluded that the contact between the compression plate and the sample was of extreme importance. As shown in figure 50, different types of shatter result if the contact

~~NO PLATE IDEAL PLATE VERY LARGE PLATE~~

FIGURE 50.—Effect of size of contact plates on the type of rupture of concrete cylinders. {From Mitchell, Mater. Res. and Standards {SOI ).) area is changed. A high compressive stress {A) at a point causes general shatter, whereas a wide application of the compressive stress (¿7) results in shearing stresses under the widely distributed load. An intermediate point {B) provides a suitable area of contact for load application. In practice, cardboard strips about l^/^ inches wide were suitable for cores 5 inches in diameter ; rubber was too soft and masonite too hard for concrete samples. Not only was the shatter altered by the material in the strips, but the stresses and strains were also affected.

~~CARDBOARD PLATE 50,000 3 40;000 Q 30,000 < 3 20,000 10,000~~

~~10 30 50 70 90 10~~

~~STRAIN (microinches /in.)~~

FIGURE 51.—Effect of the deformabmty of strips on strain gage resuUs when cardboard and masonite plates were used at the compression points. {From Mitchell, Mater. Res. and Standards {SOI ).) 78 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE A linear increase in the strain, as measured by strain gages on the sample, occurred when cardboard strips we^e used at the points of compression. As shown in figure 51, a linear increase did not occur when masonite strips were used. An application of the Mohr stress distribution theory was used to examine the stresses at the center of the sample, and "these stresses were found to be

~~«■- = (S) = ^^^, (38)~~

~~cr. = gf. (39)~~

Therefore, the compressive failure stress needs to be at least three times the tensile stress to insure tensile failure. Under point loading, o-y ranges from -^F/TTDL at the center to oo at the loading point and, unless the concentration is prevented, failure will occur by compression at the edge of the cylinder rather than by tension within the sample. The stress distributions in the sample thus indicate the need for extreme caution in selecting the loading strips employed with this method. Tension may be placed directly upon columns of soil by pulling at the ends. Hardy {17^), Nichols {313), Winterkorn {508), Gill {H6), Hendrick and Vanden Berg ( 181 ) and Willets ( 505 ) have used this method. As a rule this approach requires a prepared sample that permits grasping in order to apply the tensile stress. Wells ( 501 ) and Haefeli ( 168 ) froze attachments to the ends of soil columns to provide a means of grasping the sample. Figure 52 shows an experimental apparatus developed at the National Tillage Machinery Laboratory for applying tension forces to soil. Prepara- tion of the sample essentially precludes measuring on undisturbed soil samples with this apparatus. On the other hand, this method, as well as other methods in which prepared samples are used, is ideal for determining the factors that influence the strength of soils. Evaluation of different soil treatments may be standardized ( 2, 193, 363, m), ^ V ' ' Data obtained at the National Tillage Machinery Laboratory indicate that the direct tension method and the modulus of rupture method give the same tensile strength values for a clay soil. If this remains true for other soils in different conditions, values may be obtained that are relatively independent of the method of determination. In one interesting method for applying tension forces to soil, a block of soil is placed in a centrifuge after which the speed is increased until failure occurs ( 168, ^69 ). At failure, the force is determined from the equation F = mcù^r, (40) where m = mass, CO = angular velocity, r = radius to center of mass. SOIL DYNAMICS IN TILLAGE AND TRACTION 79

~~FIGURE 52.—Apparatus for applying tension forces to soil.~~

~~If the block is placed in an offset position, as shown in figure 53, the tensile force is applied to only one side of the block; the other side~~

~~SOIL BAR BREAK POINT~~

~~CENTRIFUGE HEAD~~

FIGURE 53.—Apparatus utilizing a centrifuge to determine tensile strength of soil. (Vomocil, Waldron, and Chancellor, Soil Sei. Soc. Amer. Proc. { 469 ).) 80 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE of the block is confined by the rim of the centrifuge head. While the sample should normally fail at the center of rotation, it may fail at some other location and the radius r must be calculated on the center of mass of that portion of the block. The acceleration force also moves the water in the soil, and this movement may affect strength at the center of the block. The tensile strength of soils may be very high—indeed, as high as that of some building materials—but this strength disappears very readily on wetting. Moisture movement, therefore, can be important. In general, tensile strength determinations have been made with the aim of evaluating the maximum tensile stress of the soil. Hen- drick and Vanden Berg ( 181 ) have also measured strain in the failure area so that tensile stress-strain relations could be obtained. A sensitive linear variable differential transformer was used to measure very small strains before soil failure. As a result, strain energy could be determined from an integration of the area under the experimental stress-strain curve. Strain has also been measured in conjunction with the beam and the indirect methods of measuring tension. Whether this can be done with any degree of ease in the centrifuge technique has yet to be determined. One of the limitations of tensile strength expressions has been the basis on which to express the force. Since only the solid or solid- and-liquid phase can support stress, the force should be expressed on this area rather than on the cross-sectional area of the soil sample. The failure area is known when the soil is in either a completely solid or a saturated condition but is not known when the soil contains air- filled pores. Eeporting force on the basis of the void ratio is some improvement but is still not exact. Unfortunately, no method has yet been developed for determining the area that transmits stress. A suitable method must be able to distinguish the bonds that have continuous materials from pseudobonds that have only contiguous materials. Low energy vibrations may serve as a means by which to evaluate, without destroying, effective bonding areas in soil. Recently, Vomocil and Waldron ( 1^68 ) have attempted to compute the tensile strength for an unsaturated system of glass beads and water based on the area of the moisture films and the soil moisture suction. Following the approach of Fisher {119, 120), the projected wetted areas of spheres were used as a basis on which to compute the tensile strength of a mass of wet beads. By using the geometry of the system at different degrees of moisture saturation, it was possible to determine a series of areas over which the tensile force must operate. When these areas were multiplied by the equivalent soil-moisture suction as predicted from capillary theory, the computed tensile strength of the mass of spheres agreed with the value determined from measurements. Unfortunately, computations based on the measured soil-moisture suction predicted tensile strengths as much as 40 times greater than those measured. Thus, there seems to be no simple way to relate soil-moisture suction to tensile strength, even in a simple system. 3.2.7.3 Compression As discussed in section 2.8.2, compression is a failure condition associated with a change in volume of soil. Eecall that failure was SOIL DYNAMICS IN TILLAGE AND TRACTION 81 defined by the state of stress at incipient volume change. Since the soil may have many densities (a measure of the volume), a stress- strain relation is required. A suitable stress-volume strain relation has not yet been established, so simplified assumptions must be made. The mathematical parameters defined by the assumed stress-volume strain relation are the defined dynamic parameters that characterize compression of the soil. Unfortunately, lack of a suitable stress- strain relation has deterred assessing compression in terms of specific parameters. Eather, the stress and associated volume are usually reported either in tables or graphs. Inability to use compression parameters in soil-machine relations, except in an intuitive sense, probably results from the fact that the sense of urgency which has been associated with the development of shear parameters has been lacking in the development of compression parameters. In measuring compression, the stress-strain relation requires that change in volume be expressed in some suitable manner. The usual procedure has been to relate stress to compactness rather than to a change in compactness. As will be verified later, the observed stress- volume strain relations are not linear, so that absolute magnitudes rather than change iñ magnitudes must, of necessity, be related. Four expressions are commonly used to define the state of compactness or compression. Where the volume of the soil is defined as the volume occupied by soil solids, water, and air, the four expressions are: (1) void ratio (volume of voids or pores divided by volume of soil solids) ; (2) porosity (volume of voids or pores divided by volume of soil) ; (3) dry bulk density (weight of soil solids divided by volume of soil) ; and (4) apparent specific gravity (dry bulk density divided by density of water). Wet bulk density is occasionally used, and it is defined as weight of soil solids and water divided by volume of soil. Methods have been developed and standardized for measuring these quantities ( ^, i^, 2Iß^ %4S^ Jp50^ i53^ J^ôlp^ Jf73 ), and they will not be repeated here. A suitable expression is needed not only for defining compactness but also for defining stresses. As indicated in section 2.8.2, six stress components are required to define the state of stress at a point so that some functional relation between the state of compactness and the six stress components is implied. Because this relation has not been established, simplifying assumptions are necessary. The assumption used will determine not only the resulting relation but also the apparatus for measuring the stress. A common assumption is that the largest principal stress is related to a change in volume. With such an assumption, the soil is usually confined in a suitable container, such as a cylinder, and uniaxial stress is applied to an exposed surface, such as one end of the cylinder. Since no shearing stresses are applied to the surface, the applied stress is a principal stress and, intuitively, is the largest principal stress. Expressing the degree of compactness for an applied stress gives the desired value. Unfortunately, the frictional characteristics of soil cause a nonuniform stress distribution, and in a narrow compression chamber arching may occur. The difficulty experienced in ramming soil through a small pipe is a manifestation of arching. As shown in figure 54, the stress measured at the bottom of a narrow, rigid. 82 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~10 15 20 25 30 SURFACE PRESSURE (psi)~~

FIGURE 54.—Measured vertical stress at the bottom of a cylinder, 3.75 inches in diameter, filled with clay soil to different depths. (Reaves and Nichols, Agr. Engin. ( 345 ).) cylindrical container is never the same as that applied to the surface. Use of containers with low depth-width ratios and lining the containers with greased, thin plastic liners minimizes the effect but does not eliminate it {66). Since the volume change must be determined for the entire sample, any irregular changes such as those that result from nonuniform stress distributions will be averaged over the entire sample. It is imperative to use a compressive system where nonuniformity is reduced to a minimum, or the measured results will not be accurate. Another assumption that has recently been proposed is that the mean normal stress is related to volume strain. Vanden Berg, Buchele, and Malvern ( ^59 ) and Harris, Buchele, and Malvern ( 175 ) have examined this possibility but have not been able to prove or disprove the assumption. Experimental verification of the mean normal stress theory requires a different apparatus to study compression because three mutually perpendicular normal stresses must be measured. One suitable device is the triaxial apparatus discussed in section 3.2.1.1. The flexible walls along the side of the sample are unable to support tangential stresses so that no shearing stresses are applied to the soil sample. Thus, the three principal stresses are measured and mean normal stress can be calculated. Recording the volume change of the soil sample by a suitable means provides the final required measurement, which is used as the output of the reaction. Irregularities in soil compression may be expected near the ends of the sample where the rigid platens contact the soil. How^ever, the irregularities are probably smaller than would be expected in a SOIL DYNAMICS IN TILLAGE AND TRACTION 83 rigid confining container. The triaxial apparatus can also be used where the largest principal stress assumption is made, since that value is also available from the measured data. Hovanesian and Buchele ( 186 ) used water pressure to apply mean normal stress to soil samples in flexible rubber containers. Such procedures provide a simple method for measuring the compressibility of soil. No standardized method can be developed until an accurate stress- volume strain relation can be obtained. Shear and vibration affect compressibility of soil and further complicate the situation. So- called kneading compactors have been developed to better account for the effects (5^, 125, Í01, -^0). The various ramifications of these devices as well as the subtle interrelations of factors affectmg compressibility are discussed in more detail in chapter 8. 3.2.7.4 P/ast/c F/ow Plastic flow is a failure condition in soil just as shear, tension, and compression are. As discussed in section 2.8.4, no criteria for failure have been established, although the phenomenon is clearly observed. Plastic-flow failure can be described in terms of shear failure except that no distinct failure surface appears; rather, the entire mass of soil in the neighborhood of the applied forces fails by deforming without any distinct separation on any surface. Be- cause no criteria for plastic-flow failure have been established, no mathematical models have been proposed to represent the forces acting at failure. Consequently, various plasticity parameters based on other criteria have been arbitrarily proposed. So-called plasticity parameters, which have been expressed in terms of moisture content of the soil (that is, the Atterberg limits), have been defined, and standard methods for making the measurements have been established ( 1^ ^7, 369, J¡SO). The moisture content of the soil where plastic or liquid failure occurs is designated, respectively, as the plastic or liquid limit. The numerical difference between these two limits is defined as the plastic index, which is generally interpreted as the range in soil moisture where the soil has the capacity to act in a plastic manner. The plasticity of soils is not separate and distinct from other physical properties ( 20,153, 332 ). Thus, in the absence of a plastic index, a general characterization of soil may be obtained from the cation exchange capacity, moisture holding capacity, or the specific area. Plastic parameters defined in terms of moisture content are not rigorous smce they are not concerned with the forces involved at failure. Nevertheless, the parameters are the only estimates presently available and are generally used. They are useful since they are defined in relation to soil behavior. With sufficient experience, an individual can translate the plastic parameters into potential soil behavior and can make a practical judgment on the characterization of the soil in terms of the parameters. Nichols ( 317 ) attempted to make the parameters more than just a characterization by^ describing a linear relation between the shearing force and the plastic parameters. Equation 41 expresses the relation 84: AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE -W) (0.06P/ + P + 1.8) i^F S -— ^P^ - (41) PI where Fs = shear stress, PL = plastic limit, PI = plastic index, P = normal stress, W = water content of soil. The maximum shear force occurred near the lower plastic limit, so that the maximum shear force could be estimated from the plastic parameters when the soil was disturbed—that is, remolded before shear force Avas measured. This equation does not hold for a consolidated cemented soil where the moisture content is varied by drying. Subsequent to Nichols' work, Croney and Coleman ( 88 ) reported that a lineal relation exists between the logarithm of the soil moisture suction (pF) and soil strength in the plastic range. They measured strength by the number of blows required to cause plastic failure with the standard liquid limit apparatus (U) as the soil was permitted to dry. The relation held for soil that was continually stirred during drying as well as for natural and initially disturbed soils. The continual disturbance created a condition in which structural bonds that were initially present were destroyed and new bonds w^ere prevented from forming. Greacen ( 161-163 ) used the equation W = -A log P' + 0, (42) where W = water content, P^ = soil moisture suction, C — water content at unit P', A = ~dW/d\ogP' (slope), to describe the Croney-Coleman type of relation. Based on a number of actual measurements, P' was considered to be approximately 10 grams per square centimeter at the liquid limit (LL) and 666 grams per square centimeter at the plastic limit (PL). Evaluating equation 42 in terms of O at the liquid limit where log P^ = 1, C = A-\-LL (43) and A as

~~A = {LL - PL)/{log f\r. - log PVL), (44) provides a means of evaluating the constants of the equation. Sub- stituting these in equation 42 and solving for log P%~~

~~logP'=l + 1.82(§f^). (45)~~

P' expresses the equivalent load on the soil during shear at different water contents. Its value depends on the assumed linear relation described earlier. SOIL DYlN'AMICS IN TILLAGE AND TRACTION 85 Greacen ( 161 ) lias proposed that the strength of the soil be described in terms of the maximum pressure that the soil can withstand without furtlier consolidation. He proposed that this load bo expressed logarithmically and defined as the equivalent strength of the soil log S. In saturated clays, where the angle of friction can be considered to be zero, the shear strength in a continuously straining soil may be assumed to be due to the applied suction P\ By definition, log S — log P' in equation 45 ; hence, the possibility exists of calculating the equivalent strength of the soil from moisture data. Plots of equivalent soil strength, as estimated from log ^ = log P', versus the logarithm of the measured moisture suction during shear did not produce a unit slope; lience complete agreement was not found in the proposed relation. That the results did not agree might be explained in part on the assumption that mechanical and suction forces are equivalent. Kesults of McMurdie and Day ( 282 ) and Vomocil and Waldron (468)^ which Avere discussed earlier, indicate that this assumption may not be valid in unsaturated conditions. Another measurement that appears to be particularly adapted for evaluating plastic strength of soft, wet soils is the Jourgenson squeeze test ( 487 ). The apparatus used resembles a shear box with open ends (fig. 55). The soil is placed in the box and squeezed by

FIGURE 55.—Apparatus used for the Jourgensen squeeze test. Open ends permit the soil to flow out under pressure. (Waterways Experiment Station (^87).) a vertical stress that causes the soil to be extruded from the open ends of the box. The shear strength of the soil is calculated by means of the equation Pa S = (46) BU (l + ira/L) where P normal load on upper plate, B width of sample, • a % sample thickness, L % sample length. The strength of soil determined by this method is not significantly different from that determined by other methods. In thé Jourgensen test, the magnitude of stress is the plastic parameter. 86 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE A pure shear device has been used by Murayama and Hata ( 306 ) to study the weakening of soil by repeated manipulations. The device was a shear box with movable walls that permitted the box to be tilted back and forth. The two horizontal surfaces were kept a fixed distance apart so that the volume of soil in the box did not change during the tilting (fig. 56). Aö* shown in figure 57, weakening in-

~~(A) (B)~~

~~FIGURE 56.—The nature of shear in the pure shear apparatus where the vertical angle is the tilting angle. z~~

~~2 3 5 7 10 20 30 50 100 200 NUMBER OF REPETITIONS N~~

FIGURE 57.—Effect of the number of shearing cycles on the degree of weakening of soil (Murayama and Hata, 4th Internatl. Conf. Soil Mech. and Found. Engin. Proc, Butterworths, London {S06).) creases as the number of cycles of shearing increases. One interesting point concerning soil weakening was observed in connection with vehicles operating on soil. It was possible to correlate soil weakening at a tilting angle of 40° with soil weakening under a tractor. This is shown as the dotted line in figure 57, but no correlations were made with vehicle performance. The speed of tilting was increased to 80 cycles per second without effect, but a greater angle of tilting reduced strength. Although much remains to be learned concerning the plastic properties of soils, the methods described here should be of assistance m pursuing this subject. 3.2.7.5 Fnction The previously discussed dynamic properties of shear, tension, compression, and plastic flow were all concerned with a failure condi- SOIL DYNAMICS IN TII.LAOE AND TRACTION 8 ( tion within the mass of soil. As discussed in section 2.9, ri

FIGURE 58—A simple slider system used to determine the coefficient of slidinK friction. 88 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE from measurements made on a dynamic sliding system. Equation 29 is then used to relate the tangential and normal stresses. Actual measurements may be made by using a simple slider system such as the one shown in figure 58. Eecording the tangential force and normal load during dynamic equilibrium provides the numerical values needed to solve equation 29. Not all sliding occurs between metal and soil ; sliders of other composition may also be used. The slider shown in figure 58 may be covered with sheets of polytetrafluoroethylene or other material that does not readily stick to soils. This simple slider iechnique has been used by a number of workers ( 89^ 93^ 286^ Jf65 ) as a means of measuring soil-metal friction. Payne ( 328^ 372 ) has used a vertical slider for field studies. With an apparatus of this type, perhaps /x^ can be measured in situ. The apparatus is similar to a vertical chisel, which can be drawn through the soil by a mobile dynamometer unit (fig. 4). A schematic diagram of the sensing apparatus is shown in figure 59. The normal load on

~~-INSTRUMENTED BEAM~~

~~TINE~~

~~-SENSITIVE PLATE~~

FIGURE 59.—The NIAE Friction Apparatus. The view on the right is a plan view showing how the sensing area was subjected only to forces caused by the soil sliding. (Rogers and Tanner ( S12 ).) the sliding surface can be altered by changing the angle of approach of the surface or by increasing the speed of operation. More complicated devices have been developed in which a ring- shaped metal surface or a circular disk wâs used. These were placed on the soil and rotated in place. Soehne ( 397 ) has used an annulus for this purpose, whereas Eowe and Barnes ( 376 ) have used a circular disk. In each device, the contact area between the soil and the slider was fixed by the physical size of the slider so that the intensity of the load was not altered during operation. Complications arise with rotating sliders because the slider operates continuously on the same soil. Structural changes present a continuously changing surface to the slider and /x' often changes. Also, travel distances may vary considerably for different parts of the slider. Use of an annulus instead of a circular disk reduces the importance of this factor. However, some average distance through which sliding occurs must be assumed. When the annulus is large and narrow, there is little difference between the distance traveled at the inner and outer edges of the slider so that the average is realistic. The coefficient of sliding friction as a dynamic parameter has been SOIL DYNAMICS IN TILLAGE AND TRACTION 89 widely applied to soil-machine relations, and some of the applications are discussed in more specific terms in chapter 4. 3.2.7.6 Adhesion Adhesion as a dynamic property was discussed in section 2.9.3. One of the unusual aspects of past research efforts has been the emphasis to relate the physical properties of soil and moisture to the adhesion phenomenon. Thus, adhesion has been theoretically determined in terms of basic relations. Unfortunately, adhesion has not been expressed in terms that can be easily incorporated into some useful soil-machine relation. In other words, the dynamic property adhesion has been related to physical properties but has not been suitably defined by a quantitative equation describing behavior. Force mputs causing the behavior have not been suitably expressed. A comparison of adhesion with friction and shear shows that in friction and shear the opposite situation exists. In friction and shear, dynamic parameters have been identified and a means has been developed for measuring the parameters and incorporating them into soil-machine relations. The parameters, however, have not as yet been related to physical properties except in gross approximations ( 315 ). Thus, the importance of identifying dynamic parameters is clearly demonstrated. Even when a reasonably accurate relation has been established between physical properties and a dynamic property, little practical use can be made of the relationship unless the dynamic property has been represented by a suitable parameter or parameters. There is no intent here to negate or minimize efforts to relate dynamic properties to physical properties. Such information is obviously necessary in order to have a complete soil dynamic theory. The complexity of this yet undetermined theory, however, dictates that parameters expressing the desired behavior in which the dynamic properties are involved should be identified first. After the parameters have been identified, physical properties can then be related to them. Not all past research efforts have attempted to relate physical properties to adhesion. But some attempts to identify adhesion in terms of useful parameters have had a measure of success. Adhesion has two important forms of behavior which must be represented in soil-machine relations. The first of these is in connection with sliding friction ; the second is in connection with stickiness. Although soil adheres to various materials, the forces required to move the soil tangentially on the surface and normally from the surface differ. An analogous situation can be visualized in the example of two glass plates held together by a film of water. The ease by which they may be slid apart is no index of the force required to pull them apart. The effect of the adhesive force on both aspects must be measured. The basic measurement of adhesion as applied to friction requires simultaneous measurement of (1) friction stress, (2) movement of the soil tangent to the interface, and (3) the normal load on the surface. Payne and Fountaine ( 331 ) have visualized soil adhesion as an additional parameter in the soil-metal friction equation 29. On this basis the equation has the form 90 AGRICULTURE HANDBOOK 316, U.S. DEPT. OP AGRICULTURE S' = O. + o- tan Ô, (47) where 8^ = sliding stress, Oa — adhesion, cr = normal stress of frictional surface, 8 = angle of soil-metal friction. A plot of S' versus cr is constructed for measurements made by methods discussed in section 3.2.1.1 at a series of different normal loads. Since equation 47 has the same basic form as the familiar Coulomb equation, the intercept was considered to be Oa. As a general rule, a straight line or a slight curve can be drawn through the points. Since tlie S' axis represents zero normal load, the residual value of S^ represents 6^„, the adhesion, and consequently is the desired parameter. The slope of the line represents tan 8, the angle of sliding friction. Payne and Fountaine thus use equation 47 as the mathematical model to represent adhesion. A different mathematical model representing adhesion can be envisioned from an analogy with a sliding magnet. Suppose the coefficient of friction between an electromagnet and steel were being determined. The friction force and the normal load could be measured as the magnet is slid along a steel surface with no current applied to the magnet. Equation 19 can be used to determine the coefficient of friction. If the electromagnet were activated and the coefficient of friction again determhied, a higher coefficient would appear to result since the same apparent normal load wôuld be applied but a higher friction force wT)uld be measured. The reason for the increase in friction force in this simple case is obvious ; the normal load wâs increased by the presence of the magnetic field. The increase in friction force thus resulted from the increase in the normal load and not from an increase in the coefficient of friction. Adhesion can affect soil-metal friction in a similar manner. Equa- tion 29 suggests ignoring adhesion and lumping it into an apparent coefficient of sliding friction. Equation 47 is an attempt to represent adhesion by Ca. If, however, adhesion acts as the magnet does in the foregoing example, a different representation can be proposed. If the added normal load that results from adhesion, which causes the increase in friction force, can be specified, then equation 19 could be written as S' = (o-i + (T) tan 8, (48) where S^ ~ sliding stress, cTi = normal stress due to adhesion, cr — mechanical stress, 8 = angle of soil-metal friction. Such a proposal is partially justified, since the equivalence of adhesion and mechanical forces on friction has been demonstrated within certain ranges by Fountaine and Payne ( 127^ 131 ) (sec. 2.9.3.). If equation 48 can be verified, the parameter needed to represent the effect of adhesion on soil-metal friction is 0*1, the adhesive stress. Since the normal stress is already reasonably well related to physical properties and sliding friction, such information can be directly applied to soil-machine relations. On the other hand, Ca would have SOIL DYNAMICS IN TILLAGE AND TRACTION 91 to be either measured or directly related to physical x^-operties by suitable means. Thus, equation 48 offers a direct means of representing the effect of adhesion on sliding friction. In nearly all applications of adhesion, the parameter Ca has been used; hence, the methods and their limitations concerning application of G, as discussed in section 3.2.1.1, also apply to adhesion. Payne and Fountaine ( 331 ) have used the adhesion parameter G a to estimate the values of the approach angle 8 of a tillage tool with the soil, at which scouring would cease. Since the point where scouring ceases is the point where soil shear begins, values of S and S' are equal. Critical values of ô for selected values of G a or critical values of G a for selected values of ô can be computed by using the relations shown in figure 119, along with known values of AS" = S\ G^ and ^. Several examples are shown in table 8. Beyond this application to scouring, little use has been made of adhesive parameters. Rowe introduced Ga into the mechanism of a simple soil-tool system, but the degree of refinement added by this contribution has not been clearly established. A number of situations exist in which adhesion is an important factor, but lack of a mechanics limits the use of the parameters when they are in such a simple form as Ga^ Since soil adheres to metals and other materials, it becomes a problem to get or keep the surface of the material free of soil. Thus, the second phase of adhesion—stickiness—becomes important. Measur- ing the adhesion parameter Gcc does not measure the tenacity with which soil is held against a surface. This force becomes important under some conditions—for example, Avhen soil sticks between lugs and grousers or other parts of tools or machinery. Under these conditions, adhesion may contribute to vehicle immobilization or substandard performance of the machine. Stickiness was recognized many years ago, and a method was developed for determining the sticky point. The moisture content at which soil would stick to a spatula was taken as the sticky point of the soil. The method does not produce quantitative data, but it does reflect the moisture-holding characteristics of the soil ( 151 ). Foun- taine ( 127 ) and Kaburaki and Kisu ( W5 ) have used methods in which a small flat metal plate was pressed against the soil after which the force required to pull the plate from the soil was determined. This value was expressed in terms of force per unit area and termed adhesion. Whether this value of adhesion is a realistic estimate of the normal component of loading in friction is unknown. Fisher ( 120 ) has made a convincing argument of this point based on the reasoning that water would move in the bonds and that Ú\Q dynamic stress during sliding would not be the same as the static stress. The value, on the other hand, does represent a realistic assessment of adhesion for cases where a similar type of removal occurs. As an example, based on this measurement, the speed at which soil could be torn from a rolling wheel could possibly be determined for a specific wheel and soil condition. Green ( 16Jp ) has studied the removal of soil adhering to root crops by dropping them and letting the momentum of the soil overcome the adhesion so as to tear free. The main objective of this research, however, was directed toward cleaning the roots rather than the adhesion problem. 92 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~^ ^ o 5 Çjj TtH CO Tt^ 00 CO Critical eg value of~~

~~II c¿ CO CO o ïO û^' T-í rH TH TtH Critical value of t CO~~

~~5 Soococo o ÍSjíO COTí^CO CD Critical value of en is« VA A «H 0 •'^* o iO o o ^ C CO 00 l>; C5 W C5 û^" TH TH -A TjH â 4.J >»~~

~~Critical -M value of A % CÖ u OJ 0 >H «H p~~

~~MíO Critical value of~~

~~■gil •^' KÎ lo o o do Oi TH 00 Oi (^' r-i~~

•^ CO n^ '?Cü -M -M S '5* ^^ O» ^•OrH CO .iH iD • o; ,r| pa .^©0 00 t>5 fl ,^^ u CÖ V^ Tt^ O CO O CÖ a OJ íO Ç55CO CO CO (M a a 0 .S 0 O -M 0 a 03 03 P -4J 02 ^=4 Co yj i3 i3 '0 «5 1 a 0 ■e- a 05 CO CO CO CO -M 03 +j ci 03 A 0) A •^ Ö a 4-> P>» 2 «O 0 ^ «H «H 0 0

0 o; Prl o C3 f3 C5 m o Oí! (M C<1 C^ '^ ^^ 0 H ç^ m SOIL DYNAMICS IN TILLAGE AND TRACTION 93 The attractive force of adhesion is determined by two factors: first, the actual strength of attraction of a unit area of bonding; second, the actual area of the attractive bonds. The pressure applied to the metal surface inñuences both of these quantities so that evaluation of the results is difficult. The adhesive values measured by the metal plate technique must have an initial conditioning loading which duplicates the actual loading of the system under study or the results will have little meaning. As shown in table 9, the

~~TABLE ^.—Efect of loading pressure on the adhesive force hetiveen soil and a metal plate~~

Loamy sand with a Clay loam with a Load on plate moisture content of2— moisture content of^- (grams) 1 24 percent 18 percent 29 percent 24 percent Gm./cmß Gm./cmß Gm./cmß Gm./cm.^ 1,590 26 16 20 40 4,590 51 17 51 56 7,590 82 19 76 57 10,590 96 38 132 60 13,590 111 30 146 66 16,590 122 35 246 84 1 A highly poUshed, chromium-plated metal disk 5 cm. in diameter was used as the test plate. 2 On an oven-dry basis. SOURCE : Fountaine ( 126 ).

adhesive force is altered considerably by the pressure used to establish contact between the soil and the test surface {126). The extent to which specific soil properties influence sticking has not been determined. A clay soil per se is not enough to dictate greater sticking. When higher loadings were applied to the plate, clay loam soil with a moisture content of 24 percent (table 9) did not display greater stickiness than loamy sand soil. Additional information must be obtained before the various aspects of soil stickiness can be understood. 3.2.2 Measuring Composite Parameters As defined in section 3.2, a composite parameter combines the effects of one or more dynamic parameters that are known to be independent. The distinction between an independent and a composite parameter depends solely on prior knowledge. Thus in form, appearance, and assessment, the composite parameter is handled like the independent parameter. The usefulness of the composite parameter is its simplicity and often its ease of measurement. Since an independent parameter often cannot be assessed, a composite parameter must be used. In attempting to use a composite parameter in a soil-machme relation, the dependence of the parameter on more fundamental factors whose actions and interactions are combined in some average by the composite must be recognized. Lack of recognition may lead to erroneous conclusions or prevent putting appropriate restrictions on the conclusions. Obviously, a complete soil dynamics theory must be 04 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE based on independent parameters; however, until the independent parameters are identified and can be assessed, composite parameters can be extremely useful. Independent properties that have been identified were discussed in chapter 2 and means of assessing them have been discussed in this chapter. Composite properties are defined here together with the means for assessing them. Basically, the process used is similar to the one used for independent properties. Behavior of soil in terms of a response to specifically applied forces is observed. A mathematical model that represents the behavior is envisioned, and appropriate parameters of the model are used as measures of the dynamic property. Penetration, bearing strength, and induced strength are examples of composite properties. 3.2.2.7 Penetration Before penetration can be discussed, a mathematical model is required to represent behavior. The behavior observed with penetration occurs when simple probes are pressed or driven into soil. Depending on the shape and type of instrument used, cutting or separation, shear failure, friction failure, compression failure, or even plastic failure, or any combination of these may occur as the instrument is forced into the soil. Since the tip or probe of penetrometers is usually small in terms of cross-sectional area (generally less than 1 square inch) and since the tip is generally larger than the driving rod, the total resistance to penetration reflects the soil conditions near the tip. Behavior can thus be described by expressing the resistance to penetration at a given depth in some suitable manner. This resistance, which is some combination of the possible failures, obviously is a composite property. The resistance is usually considered to reflect the strength of the soil. Many types of penetrometers are commercially available. Their shape and size and the technique of driving them into the soil have suggested the mathematical model used to characterize the behavior. As a result of lack of standardization in the different models, interpretation of the data reported has been difficult. With few exceptions, the penetrometer has been relegated to a position in which it serves as a means for evaluating the uniformity of a particular soil condition. To be widely used in research, penetrometers will prob- Rblj have to be standardized unless the basic mechanics of the behavior is developed. Two mathematical models have mainly been used to represent penetration behavior. One model expresses the force required to cause penetration, either in terms of magnitude or on a unit area basis. The other model measures the energy required to cause penetration. Generally, an average value over some depth is considered representative of penetration. Zelenin ( 515 ) has reported findings made on an impact penetrometer. The penetrometer had a flat, circular penetrating plunger with a cross-sectional area of 1 square centimeter ; in extremely loose soils the area was increased to 2 square centimeters. A 2.5 kilogram weight was dropped a distance of 0.4 meter to drive the plunger into the soil. Since each impact imparted 1 kilogram-meter of energy to the plunger, the number of impacts was a measure of the energy SOIL DYNAMICS IN TILLAGE AND TRACTION 95 required to drive the tip to a certain depth. For the particular penetrometer under discussion, the number of impacts C to penetrate to a depth of 10 centimeters was the parameter used to express resistance to penetration. Zelenin correlated data obtained with the impact penetrometer to data obtained with a static penetrometer pushed slowly into the soil. The parameter expressing penetration resistance for the static penetrometer was designated K^ in kilograms per square centimeter ; thus, the static penetrometer uses the first mathematical model discussed above. Figure 60 shoAvs the relation between the number of

~~20 40 60 80 100 STATIC PENETROMETER RESISTANCE (Kg/cm*)~~

~~FIGURE 60.—Relation between impact and static penetrometer. (Zelenin {515).)~~

impacts and the force required to press the static penetrometer through the soil. Each point in figure 60 represents a different soil type or soil condition and clearly demonstrates the equivalence of the two methods. Because the static penetrometer is a simpler instrument than the impact penetrometer, the majority of penetrometers have been the static type. Recording penetrometers ( 90, 172, 261, 305, 31,9, 426 ) have been developed to provide a continuous record of resistance with depth for various special purposes. Some of these have unique applications; McClelland {261 ) developed one design to measure the horizontal resistance in soils, whereas Morton and Buchele ( 305 ) developed another to simulate a seedling. In the latter, the emergence energy was computed from the measured data. As shown in figure 61, the resistance due to formation of a crust on the surface could be readily detected. Imaginative modifications of penetrometers have been developed. Aerial penetrometers ( 483 ) that may be dropped from low-flying aircraft have been designed. Culpin ( 90 ) measured the depth to Avhich revolver bullets would penetrate into the soil by passing a stiff wire into the open channel. Kondner ( 223 ) was able to reduce the 96 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~SOIL NOT Wk PERMITTED TO DRY~~

~~SOIL PERMITTED TO DRY~~

~~FORCE (lbs)~~

~~FIGURE 61.—Seedling emergence force as measured by a penetrometer. (Morton and Buchele, Agr. Engin. ( 5Ö5 ). )~~

measurements he obtained from penetrometers of various sizes and shapes to a common dimensionless basis; the basis is discussed in detail in section 4.4.2 (fig. 127). Kondner's contribution probably will extend the usefulness of the static penetrometer since results can be interpreted in specific terms. Several workers have attempted to relate penetrometer measurements to various forces they were studying. For example, Stone and Williams ( J^lJi, ) used a penetrometer to estimate the draft force of a plow in various soil conditions. They established an empirical correlation between the penetrometer reading and the specific draft of a plow. No provisions were made to apply the data to other types of plows. Zelenin ( 516 ) correlated the cutting force in soil to penetrometer size, and the correlation is discussed in section 4.4.2. Mc- Kibben and Hall ( 277 ) used penetration resistance to predict rolling resistance of towed wheels (sec. 7.8.2). 3.2,2,2 Bearing Strength The soil behavior described by bearing strength is the sinkage that results from an applied load. Settlement of building foundations is one example of this behavior; the support required by vehicles and machinery is another example. The forces acting when sinkage occurs can be represented mathematically in terms of stress expressed on a unit area basis. With few exceptions, however, the main criterion for evaluating bearing strength is depth of sinkage. Thus, while the magnitude of the applied stress could be the parameter that assesses bearing strength, sinkage is so important that a mathematical relation between the applied stress and the resulting sinkage is needed. In reality, a penetrometer could provide a basis SOIL DYNAMICS IN TILLAGE AND TRACTION 97 for determining bearing strength except for one important factor. The concept of penetration envisions a measurement of resistance as it changes with depth. Consequently, the penetrometer attempts to measure resistance near its tip. In bearing strength, however, the surface of the soil sinks ; and it is the force that acts on this sinking surface that is important. This subtle difference must be clearly distinguished to properly use penetration and bearing strength parameters. The possible modes of failure in the soil are the same for bearing strength as for penetration so that bearing strength is a composite property. Because the relative magnitude of permissive sinkage and the time for sinkage to occur are greatly different for building foundations than for off-the-road vehicles, separate mathematical models have generally been used. For foundations, an equation relating sinkage and load has been developed from the theory of elasticity ( P ). The equation is s = Gs{P/Ä){h/E){l-fi^), (49) where s = settlement of load, G s = coefficient of shape and stiffness of the loading plate, h = diameter or width of the load, A = loaded area, E = modulus of elasticity of soil, fi = Poisson's ratio, P = applied load. This equation may be rearranged into a logarithmic form and the equation is log P/A = log s/h + log l/Cs{E/l - iJ?), (50) where it has the linear characteristics of a straight line. Since the slope of equation 50 is unity, the parameter of Ú\^ equation that reflects bearing strength is the constant term i/Gs{En-ii?). The coefficient C^ can be evaluated theoretically from the theory of elasticity so that by assuming a value for /x (usually 0.5), the modulus of elasticity E becomes the parameter that assesses bearing strength. Data shown for one soil condition (fig. 62) demonstrate that the influence of size and shape of the loaded area is minimized by equation 50. The curvature of the average line and deviation from a 45-degree slope reflect behavior that is not represented by the theory of elasticity. Refinements have been made in the equation by evaluating the changing slope of the line to better represent observed behavior. Rather remarkable results have been noted. When compared in the same soil condition, 40- X 50-foot rigid test blocks have yielded the same load deflection curves as 8-inch diameter bearing plates. However, these results are not always obtained, so that additional refinements and even different mathematical models are being sought. The apparatus to assess the conditions represented by equation 50 is relatively simple. As has already been implied, generally a round 98 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE PLATE DIAMETER (in) lOOc

~~JP A 10:~~

~~I I I III11 ' ■■■■■■ -I 1 I I I Mil 0.0001 0.001 0.01~~

b FiGUBE 62.—The relation between applied load and ratio of settlement to diameter for four plate diameters. (Amer. Soc. for Testing Materials {9 ).) rigid plate is suitably controlled so that it can be loaded in increments and allowed to settle to equilibrium. Equilibrium is generally adjudged to occur when the rate of settling is 0.02 inch per hour or less or when the load has been applied for a total of 30 minutes. The biggest difficulty is obtaining a means of applying the load. One often-used means has been a large truck, carrying up to 50 tons. When shorter loading times and larger sinkages than in building foundations are involved, the Bernstein equation ( 24S, 2^8 ) is the generally accepted mathematical model for bearing strength. A wheel having a contact area 1 foot long and traveling at 5 miles per hour applies its load to a given area of soil for only 0.14 second. Since many soil-moving operations are accomplished at about 5 miles per hour, rather short periods of time are always involved. The basic equation as proposed by Bernstein has the form P = k{^^), (51) where P = pressure on the soil, k = ù> constant, 3 = depth of sinkage, n = a constant. The parameters k and n when isolated from this equation are the measures of the dynamic property, bearing strength. The value n expresses soil characteristics whereas k expresses loading area as well as soil characteristics. In any given soil condition, n is considered to remain the same for all loading areas. Because of the effect of the SOIL DYNAMICS IN TILLAGE AND TRACTION 99 shape of the loading area, Bernstein's h was further divided to provide a cohesive component ¿c, which was considered to be a function of the size of the loading area, and h^ a frictional component, which was independent of the loading area. The component he was divided by 5, the width of the loading area, as a simplified means to represent the effect of the loading area so that h in equation 51 becomes k = {h/i + k^). (52) In the revised form, the modified Bernstein equation appears as p = (hJl-\-'k;)z^, (58) Equation 53 is the most widely used model of bearing strength for soil-moving operations, and the three parameters ^c? h^^ and n are a means of assessing the composite property, bearing strength. An apparatus for assessing bearing strength, as represented by equation 53, generally provides a means for applying a load to a plate of known dimensions and simultaneously measures the load and sinkages as the plate is forced into the ground. Various means of obtaining the measurements have been proposed; one often-used method was reported by the Land Locomotion Laboratory (^^5, 2Ji,8 ). Generally at least three sizes of plates are used for a given soil condition. The parameters of equation 53 can be evaluated most easily by constructing a logarithmic plot, as shown in figure 63.

~~LOG z~~

~~FIGURE 63.—Logarithmic plot of Bernstein equation from which 7c and n can be determined.~~

Given a series of h values, equation 52 can then be plotted as shown in figure 64, since equation 52 is of linear form having a slope of he and an intercept of h^. When calculations can be performed by machines, simultaneous solutions of equations 52 and 53 will give the values of the parameters. In practice the data do not always produce straight lines, or the lines may not be parallel as they are shown in figure 63. Such deviations indicate the inadequacy and inaccuracy of the modified Bern- stein equation. Presumably a more complex equation could be 100 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~T Í~~

~~FIGURE 64.—Graphical solution of equation 52 to give values of kc and k..~~

devised; however, such an equation will require even more complex mathematical operations so that the added accuracy must be balanced against the added complexity. Since bearing strength is already known to be a composite property, a more complex representation may be impractical ; thus, equation 53 is generally accepted as a satisfactory compromise. One recent attempt to evaluate bearing strength has followed a slightly different approach. Since bearing strength is a composite property, an interaction can be expected to occur with other dynamic properties. In traction, a vehicle induces a combined reaction that requires shearing resistance in a horizontal direction as well as bearing strength in a vertical direction to prevent sinkage. Dickson ( 102 ) has developed a tilting plate penetrometer to simulate the action of a vehicle and create a representative soil reaction. Soil resistance to penetration of the plate was measured as the plate was forced into the soil along a tilted axis. Control of the tilt angle and the load on the plate simulated a soil movement that represented the effects of horizontal slip as well as those of vertical sinkage. This is obviously an attempt to assess specific soil behavior in terms of a composite of composites. This approach may simulate overall behavior of a soil-vehicle system more closely than one that embodies the simultaneous but assumed independent dynamic properties of shearing and bearing strength. If reasonable accuracy and simplicity are obtained, the approach merits further investigation. On the other hand, if the approach does not yield new information that aids in identifying independent dynamic properties of soil, its research value may be limited. Only by identifying such properties can we further our understanding of how and why the soil-vehicle system behaves as it does. 3,2.2,3 Induced Strength One of the complicating behaviors in ^oil is its change in strength when it is subjected to mechanical forces. In metals, this behavior has often been termed strain hardening and, as the name implies, increases in strength may accompany movement. Observation generally confirms the implication. In soils, however, strength may SOIL DYNAMICS IN TILLAGE AND TRACTION 101 either increase or decrease, and the change is often much larger than in metals. An example of the phenomenon is the manipulation of snow into a snowball, which results in a severalfold increase in strength. In all materials, induced strength is affected by the physical properties of the material as well as by the applied forces so that both must be considered. Stress-strain relations provide one suitable means for mathematically undertaking a simultaneous consideration of both factors. As has already been stated, however, accurate stress-strain relations are not available for soil. Attempts to measure induced strength by other means have not successfully identified parameters that assess the dynamic properties of induced strength. Eather, the attempts have assessed the interaction of the manner of application of the applied forces and the resulting change in strength. Consequently, the results are composite assessments of the behavior. Shear has been used in nearly every attempt to assess changing strength. The parameters of equation 18 (discussed in sec. 3.2.1.1) thus become the measures of induced strength. One exception has been made in connection with traíRcability, in which soil resistance is measured with a cone penetrometer before and after the soil is subjected to a specified amount of manipulation that expressly represents vehicular traffic on the soil. The second measurement assesses any change in strength—that is, induced strength. In shear, the change of strength is usually represented as a change in cohesion, since the angle of internal friction generally is assumed to remain constant. T i Shear may be measured both before and after some standardized manipulation of the soil to assess the change. Since shear is actually a manipulation of soil, a special interpretation may be applied to the shear data to determine two values of cohesion. An example is Payne's residual cohesion (sec. 3.2.1.1). Two values of cohesion were developed from his initial measurements without any special manipulation of the soil. The second value, of course, was based on a decrease in strength because of a disruption of bonds in the soil during shear. A clear example of the before and after measurements is available from Transportation Research Command data ( Í32, J^SB ). Two distinct values of cohesion were proposed to reflect induced strength. Precollapsed cohesion would reflect the initial strength, whereas postcollapsed cohesion would reflect the strength after a load had been applied. Any difference between the two values would be a measure of induced strength. The only difficulty with the concept lies in measuring postcollapsed cohesion, which obviously depends on the load that is applied. Since the postcollapsed value can be determined only after the applied load has been removed, a misleading value of cohesion can be obtained. Thus, from a practical standpoint, the concept has a limitation because generally there is little need to know the strength after the load—say, a vehicle—has passed over the soil. Furthermore, the possible interaction between the soil and the apparatus that measures shear limits the practical aspects of the To avoid these difficulties, an average or relative cohesion Creh concept. 102 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE was proposed that would reflect the desired cohesion in the appropriately loaded state. An example of the concept is shown in figure 65, where sinkage of various plates into snow is correlated by assign-

10 - 10 Orel 12 in DIA. PLATE ■ 9 in DIA. PLATE 8 l2mDIA.PLATEv r cr|ü 8 - -o-6 in DIA. PLATE 9¡nDIA. PLATE \ V 1 . -x-3in DIA. PLATE /f ü 6 6 in DIA. PLÀTEv X y 6 V 3¡n DIA. PLATE. /\/ /.48 i or 4 4 a § 2 --.32 -j 2

~~-^^T^^ 1 . 1 . 1 . 0 0 ■^^i 1 • 1 . 1 , 04 0.8 1.2 1.6 "¿0 0.4 0.8 1.2 1.6 20 z PLATE PENETRATION--f PLATE PENETRATION d d (A) (B)~~

FIGURE 65.—A, Pressure on plates versus sinkage in deep dry snow. B, Same data as in A corrected for relative cohesion Crei. (Transportation Research Command ( ^55 ).) ing an appropriate value of relative cohesion. The relative cohesion was not measured but was arbitrarily assigned to provide the best fit. The fact that the data could be correlated demonstrates the practicality of the concept. Application of the concept to trafficability is discussed in section 7.8.2. 3.3 Measuring Gross Dynamic Behavior As stated earlier, many dynamic properties have not been identified. Nevertheless, characteristic and repetitive behavior patterns have been qualitatively observed, and the practical importance of these behaviors has resulted in attempts to assess them quantitatively. Since the dynamic properties in soil behavior have not been identified, other means have been used to measure the desired quantities. In some cases, no mathematical model can be envisioned; consequently, some highly empirical correlation that assesses the desired quantities is attempted. For example, forces are involved in the wear of tillage tools and, obviously, these forces appear only when movement occurs. Qualitatively, not only does wear occur but also the rate of wear is more rapid in a sharp-grained sandy soil than in a clay soil. There must be dynamic properties that characterize the forces and wear, but they have not been identified. Other examples of active soil behavior are rupture or separation of the soil mass and soil displacement. In both examples, forces are involved and movement must occur before the behavior is observed ; thus, both can be characterized by dynamic properties that have not as yet been identified. SOIL DYNAMICS IN TILLAGE AND TRACTION 103 Because these types of gross soil behavior seemingly are important in tillage and traction, crude assessments have been made to provide a method of control and evaluation that has practical usefulness. Some of these gross behaviors are discussed in the following sections, but they represent no final solution to the problems. Actually, they merely represent a starting point for additional work. 3.3.1 Rupture When brittle soils are strained severely, the result is a shattering or rupture—often called pulverization. Indeed, one of the main objectives of tillage is to cause pulverization; therefore, assessing the degree to which a tillage action affects pulverization is important. Pulverization results from shear failure, tensile failure, impact forces, and possibly other complex force distributions between a tool and soil. The complexity of the forces is one impeding factor in identifying dynamic properties of rupture. The importance of assessing the behavior can be demonstrated from qualitative observations. When soil strength is low, various tillage actions often create the same final conditions. On the other hand, when strength is high, gross differences in final conditions are often observed. The importance of determining the effectiveness of various tillage tools or combinations of tools dictates that rupture be assessed. An obvious means of evaluating the degrees of rupture is to measure the size of clods into which the continuous mass of soil is pulverized. Such a measure, however, does not assess the forces involved. On the other hand, measuring the total soil forces acting on the tillage tool does not assess rupture, since there is no evaluation of what the forces did to break up the soil. A simple correlation between clod size and draft force is not sufficient for assessment. Consider the following hypothetical possibility in comparing two tools. The tool having the higher draft requirement may also produce smaller clods. Neither tool can be rated superior because the tool that has a lower draft requirement, which is desirable, obviously does less work on the soil. One recently developed approach to assess rupture is based on energy principles. Marshall and Quirk ( 292 ) investigated clod shatter and cutting. Gill and McCreery ( H9 ) developed a method to logically relate measurements of clod size and soil forces on the basis of energy. The method does not involve dynamic properties or even a composite dynamic property. In fact, the method can be applied only to a soil-tool svstem and therefore may be considered a method of evaluating performance. In the method proposed by Gill and McCreery clods were dropped on a rigid surface and then screened to evaluate clod size. The kinetic energy expended per unit weight of soil provided a means of interpreting the results due to differences in the size and weight of samples. By repeated droppings, different amounts of energy could be used to shatter the clods and an energy-clod size relation could be obtained for a given soil condition. The technique can be used only when the soil is sufficiently cohesive so that complete shatter does not occur with one drop. The height of drop must be adjusted so that impact shatters the bonds in the soil, or the energy will be ineffective. 104 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Typical data obtained from the drop-shatter method are shown in figure 66. The data are characteristic of a soil in only one condition and any change in moisture, density, or other factors would require another determination of the energy-clod size relation.

~~0.4 0.6 0.8 1.0 1.2~~

~~LOG INPUT ENERGY (Ft-Lb/Lb)~~

~~FIGURE 66.—Relation between drop energy and clod size as represented by mean weight diameter. ( Gill and MeCreery, Agr. Engin. ( 149 ). )~~

The energy-clod size relation can be used as a basis for determining the amount of effective work done to a particular soil by a tillage tool. As an example, if a plow shattered the soil represented in figure 66 from initial clod size X to final clod size Y, the equivalent energy required to break up the soil could be determined. The input energy for the plow can be determined from the draft and speed and expressed on the unit weight of soil disturbed. For rotary or other tools, torque energy would also be included. A ratio of the energy required to operate the tool in the soil to the equivalent energy required to cause the same degree of shatter would be an index of the efficiency of the tool (table 47). Thus, a basis is provided on which to evaluate the tool. Both similar tools and widely different tools can be compared on this basis. An example of an evaluation of different tools is given in section 4.5. The drop-shatter method does not measure the absolute energy required for pulverization since the actual mechanism of failure in the drop shatter method may be different from that in an actual tillage system. Nevertheless, the principles are sound and the method will be useful even if it evaluates rupture by an indirect approach. SOIL DYNAMICS IN TILLAGE AND TRACTION 105 In another method, the rupture strength of soil has been determined by placing a small balloon in the soil and noting the inflation pressure at which the surface of the soil ruptures. Bowen {51) has used this method to study emerging plant seedlings, but its use is not restricted to this application. The principal advantage of the method is that it can be used to measure the rupture strength of a relatively undisturbed soil. If the measuring device is mserted when the soil is initially fitted into a desired condition, no further disturbance is required before making the measurement. Indeed, placement of the balloon at seed depth would provide an average of any variation in strength due to factors such as crusting, drying, and soil textural differences that occur in the soil profile. Rupture of materials has been empirically determined by a number of simple tests, but their use has not been extensive. Chepil ( 71 ) has used the change in particle size caused by a number of sievmgs as an index of mechanical stability, which in turn reflects rupture. Stewart {U^) has standardized a tumbling test for pellets that could be adapted for evaluating breakup of small aggregates. Both of these methods require some type of particle-size assessment to determine the effect of the mechanical action on the soil. The actual mechanics of breaking is never quite known in these tests, so their usefulness is limited. Thus, until the dynamic properties involved in rupture are identified, assessing rupture will depend on empirical methods. 3.3.2 Blast Erosion On occasion, soil is eroded by a type of blasting action that is exhibited when sand blasting is used to clean metal surfaces. In addition to the obvious example of wind erosion, the exhaust blasts of aircraft engines and, recently, rocket engines also cause erosion. In this type of erosion, the abrading material is usually the soil itself. Since both movement of the soil and forces to cause movement are involved, the phenomenon is properly classified as dynamic behavior. Although the behavior has been widely studied {69-72^ 4^-^)? no dynamic properties have been identified to describe the phenomenon. Eather, physical properties have been used in an empirical manner to provide an indirect means for assessing the behavior. Perhaps the most widely studied type of blast erosion is wind erosion. For erosion to occur, surface soil particles usually must be loose, dry, and small enough so that they become mobile in an air stream. Chepil ( 72 ) reports that the particles become mobile, not in relation to the actual velocity of the air stream but rather in relation to the rate of increase in velocity with height. This behavior is based on principles of aerodynamics which indicate that the velocity of air will be zero near the surface and will increase with height above the surface. This rate of increase in velocity is often termed drag velocity. Chepil defined the drag velocity just sufficient to cause a given particle to move as the threshold drag velocity. He demonstrated that threshold drag velocity is related to particle diameter, and for particles larger than 0.1 millimeter m diameter the relation is 106 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

y' = A ^[—^)gd, (54) where V^ = threshold drag velocity, ^ = a coefficient whose value depends upon the range of size and soil particles on the surface, or — bulk density of the particle, p = density of eroding fluid, g = gravitational constants, d — diameter of the particle., When the soil surface is not dry, moisture films provide a cohesive force and the particles tend to adhere to the surface. Equation 54 must then be modified so that

~~y = A ^(^:H^ (55)~~

where c = resistance due to the cohesive force. Chepil was able to demonstrate that the value c could be related to an equivalent moisture content of the soil. With a means of predicting when a soil particle would be carried by air to act as an abrading material, blast erosion could be further related to the soil. Representing the abrasion process mathematically can be compared to the chain reaction associated with a nuclear ex- plosion. As soon as the first particle on the surface of a soil is moved by the airstream, the particle strikes another fixed particle. In the process, an impact force probably much greater than the force of the moving air is imparted to the fixed particle. This bombard- ing process continues in a manner analogous to a chain reaction so that soon the airstream is literally filled with particles and erosion proceeds at a very rapid rate. A mathematical model to represent the situation is obviously difficult, and this difficulty has to date prevented defining a dynamic property of blast erosion. In lieu of a mathematical model, Chepil defined a coefficient of abrasion as a measure of the susceptibility of soil to blast erosion. The coefficient is the quantity of soil material abraded per unit weight of abrader blown against the aggregate in a 25-mile-per-hour windstream. The coefficient can be determined only in a special apparatus wherein the necessary measurements can be made. Using this special apparatus and briquets made of particles of dry soil of diiferent diameters, Chepil determined a relation between the coefficient of abrasion, the modulus of rupture (sec. 3.2.1.2), and particle diameter, as shown in figure 67. The extent to which this relation may be extended to other soils is not known, but presumably the relation should be rather general as long as the moisture content is controlled. As figure 67 shows, blast erosion is not assessed in terms of its own dynamic property, but it does appear to relate to the dynamic property tension. The tensile property has not been directly related to behaviors described by equations 54 or 55, but rather to the volume of soil loss. Because of the ill-defined nature of the inputs and outputs of the behavior relation, blast erosion is assessed indirectly in terms of gross behavior. SOIL DYNAMICS IN TILLAGE AND TRACTION 107

~~- \,^MODULUS OF RUPTURE~~

~~20 - ^X y^ - 10 \ y/ : \, / I UJ \ ^COEFFICIENT - in Q: < ID \ / OF ABRASION. 2 -~~

~~DIAMETER OF PARTICLE (mm)~~

~~FIGURE 67.—Relation between the modulus of rupture and the coefficient of abrasion of soils by windblown particles. ( Chepil ( 12 ). )~~

However, physical properties, not dynamic properties, are involved in equations 54 and 55 so that if a relation is determined in the future, dynamic behavior may not be fully described. The practicality of the approach, however, is demonstrated in figure 68. Figure 67 indicates that fine-grained soils are less susceptible to erosion than coarse-grained soils, and the data in figure 68 tend to support the conclusion. Furthermore, the definition of the coefficient of abrasion implied that soil loss should be proportional to the amount of abrader—that is, the curves in figure 68 should be

~~6000 X —FINE SANDY LOAM o — LOAM A—SILT LOAM (A) 5000 • —SILT LOAM (B) A—SILTY CLAY~~

~~E 3 4000~~

~~O "^ 3000 z g < g 2000 <~~

~~1000~~

~~1500 2500 ABRADER (gm)~~

FIGURE 68.—The loss of soil by abrasion as influenced by the amount of soil abrader in the windstream. (Chepil, Soil Sei. ( 7i ).) 108 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE linear. In spite of the success of the present assessment of blast erosion, the exact mechanism of the battering action of the abrasives is not fully understood. Presumably the action is different from that of sliding abrasion ( llJf ). Until the dynamic properties of blast erosion are identified, the exact mechanism representing the behavior cannot be understood. Not all blasting fluids contain abrasives; jet streams by themselves have been used to elutriate soil {69)^ reduce friction in the soil {AO)^ separate tubers ( 222 ) ; inject materials into soil {17 )^ and secure thrust for vertical takeoff aircraft ( 1^3Jf, ). The basic approach is to consider the system analogous to that of a particle moving through the fluid. Arya and Pickard {17 ) concluded that the resistance of soil particles to penetration of a high-velocity jet could be approximated by the equation R = h d^v^, (56) where R — resistance force, h = 2i constant, d — diameter of the particles, V — velocity of the jet. The nature of the jet determines the type of movement of the soil particles (fig. 69) and the effectiveness of the jet blast. The depth

~~fTTTTTTnir^~~

~~(A) (B) (C)~~

FIGURE 69.—A, A large particle displaced without rotation by a small jet directed through the center of gravity. B, A large particle rotated and moved by a smaU jet that applies an eccentric load. 0, A velocity gradient in a large jet causes rotation of particles. (Arya and Pickard, Agr. Engin. (Í7).) of penetration of a vertical jet into a column of uncemented beads increases with decreasing particle size (fig. 70). Apparently more energy is wasted in direct impact in large particles than in small particles. Theoretically, the total drag force should be the same. The more favorable penetration in fine particles should not be taken as an indication that the action would be more effective in fine- SOIL DYNAMICS IN TILLAGE AND TRACTION 109

~~6 1 ^~~

~~Í 3 UJ I 2~~

~~100 200 300 400~~

~~DIAMETER (Microns)~~

FIGURE 70.—Effect of size of particles on the depth of penetration of a jet into uncemented glass beads at several pressures. (Arya and Pickard, Agr. Engin. ( Í7 ).) textured soils in the field. Cohesion genetally increases in finer textured soils so that an increase in resistance to abrasion, as shown in figure 67, should be expected. Probably once the blast has started, detached soil fragments are mobilized to constitute an abrading charge in the jet and thus increase its boring effectiveness. Cykler and Tribble ( 91 ) have used the blast principle to inject soil fumigant through a heavy mulch paper and into soil to depths as great as 10 inches. The kinetic energy of the liquid ranged from 7 to 77 foot-pounds, depending on the velocity and weight of the in- jected charge. At least 14 foot-pounds of energy appeared to be necessary to penetrate the mulch paper (fig. 71). Additional research is required to develop measurement techniques that will provide a basis on which to predict the effectiveness of blast erosion. Desirable parameters must include characteristics of the jet as well as the soil. Until such parameters are identified, blast erosion must" be assessed in terms of gross behavior. 3.3.3 Abrasian The dynamic action of soil sliding over a metal surface (abrasion) involves more than the mechanical loss of the metal due to friction. Under high normal loads, soil particles scratch, cut, and gouge the surface to w^ear it away. Note that we are now concerned with a different behavior than in blast erosion. During erosion, the soil itself was eroded, whereas in abrasion a second material', usually metal, is involved. It is important tct assess the erosion of this second material in terms of iho^ abrasive characteristics of the soil. As discussed in section 2.9.4, the interaction of soil and metal during abrasion is highly complex. The soil generally cannot be characterized as a rigid body, and the evidence of cutting and scratching indicates that the forces within even small areas must be highly com- lio AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~• 10 -- • - • 3 ® --^ • z • o •~~

~~01 • H UJ r^ S 4 - Û- • / 2 - /~~

~~./ 1 • 1 L.. 1 10 20 30 40 50 60 70 KINETIC ENERGY (Ft Lbs)~~

FIGURE 71.—The influence of kinetic energy of a liquid jet on the depth of penetration through paper and into soil. (Plotted from Cykler and Tribble, Amer. Soc. Agr. Engin. Trans. {91 ). ) plex and of varying magnitude. Consequently, no realistic mathematical model representing the behavior has been developed, and correlations between empirical wear tests and field experience have been used to assess abrasion. Since final results (quantity of material lost) rather than a specific mechanism have been used, the assessment is properly categorized under gross behavior. Key factors that must be considered in developing and using an abrasion test include: the time and kind of contact between the soil and the material ; the normal load on the abrading soil ; the soil and surface material ; the temperature at the interface ; and the speed of the sliding action. Under some conditions, such as during plowing, the soil along the surface is continually replenished by a fresh supply of sharp grains as the tool slides along. This is not the case in a bearing where the same material acts as the abrading material indefinitely. During the abrading process the particles may be ground up and worn smooth so that their abrasive characteristics change. When the load on the soil particles exceeds their strength, they may be crushed ; and a different wear patterni results, as shown in figure 72. In an empirical test, therefore, the load on the soil particles as well as other service conditions must be the same as those on the tool, or correlation of the results w^ill be difficult. A number of techniques have been devised to evaluate the wear of different types of materials in soil. Eeed and Gordon ( 369 ), Mohsenin and others ( 302 ), Lechner and McCoUy ( 252 ), and Cooper and McCreery (81 ) have conducted experiments under laboratory and field conditions which indicate that materials may be selected by such an evaluation program. In all of the methods wear was assessed in terms of quantity of material lost for some standard condition. SOIL DYNAMICS IN TILLAGE AND TRACTION 111

~~.15~~

~~.13~~

~~.11~~

~~if) O .09~~

~~< .07 NORMAL LOAD .05 12 Lbs. .03~~

~~.01 2 4 3 9 15 21 27 TIME OF WEAR (min) NORMAL LOAD (lbs)~~

~~FIGURE 72.—Effect of a crushing load on the abrasiveness of sand particles in in a wear test. (Reed and Gordon, Agr. Engin. ( S59 ).)~~

Fairbanks ( llJf ) has attempted to measure the wear of plowshares by a radioactive tracer technique. Small metal sections of plowshares were removed and radiated to make them radioactive. They were then welded into their proper positions in the plowshares. After operation in the field, particles detached from the plowshare by wear were detected in the soil by means of suitable counters ; the amount of radioactivity was considered to be an indication of the wear. The success of this method awaits completion of additional research. Other techniques might be required for rubber or plastic compounds, but little research has been conducted on these materials. Good correlations between laboratory and field tests have been difficult to establish for tillage tools. Undoubtedly this difficulty is encountered because of the great variety of soils and soil conditions under which tillage tools operate. Measurements of hardness of the materials do not correlate as well with measurements of wear as with the observed microstructures of the metal. High percentages of primary alloy carbides have high resistance to soil abrasion, irrespective of the normal hardness values {8). It may be possible to correlate the hardness of individual particles, such as Austenite crystals, with wear by a microhardness Knoop test, whereas the overall matrix hardness as determined by a gross test, such as the Rockwell, would indicate no relation. Specific research is needed on this point. The foregoing assessments are based on the concept that a material can be selected that offers maximum abrasion resistance for all soils. The result is that various materials are subjected to a standard abrasive procedure and evaluated. Since the procedure itself influences results, the attempted correlations with material properties may be questioned. Another approach is to study the abrasive characteristics of soil. If a standard metal material can be evaluated in various soils, perhaps the soil itself may be correlated with wear. Presumably, a 112 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE geographical map showing soil abrasiveness could be effected and utilized to select special abrasion-resistant tools. Few attempts have been made to relate soil characteristics to abrasion. According to Gavrilov and Koruschkin ( IJfO ), Shchuch- kin has reported an increase in soil-metal friction with a decrease in percentage of soil fractions less than 0.01 millimeter (fig. 73).

~~BEFORE RAIN 0.5 AFTER RAIN~~

~~0.3~~

~~FRACTION < 0.01 MM (7o)~~

~~FIGURE 73.—Relation between fineness of soil particles and coefficient of friction. ( Gavrilov and Koruschkin ( IJfO ). )~~

The hardness of pure minerals has been measured and classified in terms of empirical scales ( 68^ 259 ). These data have limited value, however, since the minerals in a soil may not be pure and their hardness may be expected to vary. Carpenter and Deitz ( 62 ) report a method for sorting nonsymmetrical particles that might be of assistance. No data are available for correlating shape of particles to wear. Other factors also may be expected to inñuence abrasive wear, but concrete evidence is not available. Any characterization of soil for assessing abrasiveness should include : first, parameters that reflect the sharpness ( ^91 ), hardness, and other abrasive characteristics of the individual grains; second, parameters indicating w^eight or shear strength that would influence the magnitude of the normal load operating on the abrading particles; and third, tool parameters that would further influence the normal load on the abrading surface. A fourth strength factor governs the rigidity with which the abrading particles are held by the soil matrix. Additional knowledge is required to more fully understand and characterize abrasion. Even in terms of gross behavior, only slight progress has been made. SOIL DYNAMICS IN TILLAGE AND TRACTION 113

3.3.4 Movement The condition of the soil at one time as compared to another might be described in terms of its overall location or configuration. This is not the same type of description that might be used to describe the internal arrangement or soil structure—that is, the size and shape of the aggregates and how they are packed together. Instead, the relative location of different parts of the general soil mass are of interest. As an example, a lowering of the surface of the soil would indicate that subsidence or compaction of some form had occurred. In other cases, the soil may be inverted or moved as in plowing, harrowing, or land forming and it would be important to trace the movement. This movement can be seen in a plowed furrow, yet the movement is not easy to describe. A study of the movement in detail requires the use of some reference system so that the initial and final locations may be identified. Strain, as discussed in section 2.3, provides a rigorous model for describing movement and final location in terms of initial locations. As was pointed out, both rigid body movement—including rotation and translocation—and strain are required for a suitable description. But the mathematics becomes very complex even when simplifying assumptions are made, and little progress has been made in using strain to describe movement. Kather, initial and final locations are identified in some suitable reference system so that gross movement is observed. The movement is usually not even directly associated with the soil itself as a means for characterizing the soil—that is, a movement dynamic property. Instead, the movement is used to qualitatively observe the behavior of the interaction of soil and some device or machine. The initial and final locations of soil have been assessed in several ways. Nichols and Eandolph ( 320 ) placed aluminum foil marker strips in the soil so that movement of the soil would move the strips. The degree to which this material would alter the soil reaction would depend on the strength of the aluminum and the amount of strain in the soil. Other workers have used noncontinuous tracers such as colored beads, brass rods, sticks, gypsum, and coal dust {90, 138. 200, 267, 418 ). Both line and grid patterns of these materials have been used to mark the soil, depending on the object of the study. These tracers must be placed in the soil very accurately before soil movement is initiated. By carefully cutting the soil mass apart after a specific operation has been completed ( 100, 251, 300 ), the final position of the markers can be determined. The movement of the soil can be inferred from a simple plot of the tracers. Figure 74 shows the nature of soil movement caused by a moldboard plow. The description does not indicate the paths traveled by the individual markers. Figure 75 shows a glass-sided box technique in which the soil particles themselves serve as tracers. Although this technique has limited application, it provides a means by which a continuous path of movement can be observed. The visible lines are caused by the movement of individual particles or aggregates of soil along the glass side of the box. The particles scrape the fine layer of aluminum 114 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE I

~~^ 0 L~~

~~UJ 3 - > o < -1 2 - LU~~

~~t- 13 • 4 1 - z X (B)~~

~~3 DISTANCE (Ft)~~

~~FIGURE 74.—Markers used to trace the movement of différent portions of a mass of soil by tillage tools. (Nichols and Reed, Agr. Engin. ( 32S ).)~~

FIGURE 75.—The scratching of an aluminum-coated glass plate showing the movement of soil under loading. SOIL DYNAMICS IN TILLAGE AND TRACTION 115 from the glass so that the path of the particle in contact with the glass is recorded. Figure 75 represents the total movement that occurred in the soil as a rectangular probe was forced into the soil along the glass. Movements do not occur simultaneously and only a series of such pictures would show the progress. The extent to which this movement would occur in the soil if the glass side were not present has been questioned. When the glass is lubricated, possibly the movement of soil near the glass is relatively similar to that which would occur if the glass were not present. When glass is not used or when the tracers are not visible, their location must be determined by other means. The use of lead shot in soil has permitted determining their progressive location by means of X-rays without destroying the soil mass ( 217^ iOJf ). Photographs can be prepared to show the location of the individual shot after various increments of soil movement. Swietochowski, Bors, and Przestalski ( 1^17 ) used radioactive shot from which gamma rays emanated. These rays impinged on photographic paper to mark the location of the shot sources. Unless the location of each shot is determined as movement progresses, their direction of movement cannot be determined. Fairbanks ( IH ) used plowshares containing radioactive materials so that particles which were worn from the plow could be detected in the soil with radiation detectors. Because the worn material would be attached only to soil that slid on the plow surface, soil from that particular layer could be identified. Phosphors are materials that emit visible light during or after radiation by ultraviolet light. Staniland ( Í09 ) and Wooten, Mc- Whorter, and Eanney ( 512 ) have used ñuorescent tracers to study the efficiency of cultivation methods. Under field conditions, an ultraviolet light has been used at night to illuminate ñuorescent tracer materials so as to be able to study the degree of soil mixing caused by different tillage tools. Martini ( 293 ) used plaster markers to identify the initial center of gravity of a section of a furrow slice. He caught the plowed soil in a large pan placed in the bottom of the furrow and then balanced the pan to redetermine the center of gravity of the final position of the soil mass from the test section. He considered the difference in the location of the center of gravity as an index of the soil reaction to the plow. The configuration of the soil must often be altered into some specific form for a special purpose. A description of the surface is easy when the shape is simple. The most accurate method used is to measure the elevation of each point of the surface in reference to some base point. A surface contour map can be constructed from the data. The field survey method is the most practical for describing large areas such as those in which land forming, grades, and water courses are of interest. Mech and Free ( 296 ) and Soehne ( Jt02 ) have studied relatively rough plowed surfaces by a version of this method. At least one device is commercially available for measuring the irregularities in surface profiles of highways and airfields ( ^7 ), but this apparatus is not adequate for most detailed 116 AGRICULTURE HANDBOOK 316, U.S, DEPT. OF AGRICULTURE studies. Schäfer and Lovely ( 380 ) developed an automatic-recording soil surface profile meter. Changes in elevation have been interpreted in terms of surface roughness when a baseline was chosen at the highest or lowest point of contact. While all these methods have been used to some extent, there is need for developing better methods to determine the location and configuration of soil. 4. MECHANICS OF TILLAGE TOOLS

4.1 Introduction Tillage tools are mechanical devices that are used to apply forces to the soil to cause some desired effect such as pulverization, cuttmg, inversion, or movement of the soil. Tillage tools usually produce several effects simultaneously. The ultimate aim of tillage is to manipulate a soil from a known condition into a different desired condition by mechanical means. The objective of a mechanics of tillage tools is to provide a method for describing the application of forces to the soil and for describing the soil's reaction to the forces. An accurate mechanics would provide a method by which the effects could be predicted and controlled by the design of a tillage tool or by the use of a sequence of tillage tools. Furthermore, the efficiency and economy of the tillage operation could be evaluated from the mechanics. A thorough knowledge of the basic forces and reactions is required to develop the mechanics. Such knowledge is not available at present, and soil reactions cannot even be predicted, let alone controlled. As a result, an operation is performed, the conditions are arbitrarily evaluated, and additional operations are performed in sequence until the conditions are adjudged to be adequate. Thus, today, tillage is more an art than a science. Progress has been made, however, in developing mechanics where simple tools or simple actions are involved and where forces and reactions can be described. This chapter presents several approaches that have been used to develop simple forms of soil-tillage tool mechanics. Only homogeneous soil conditions are considered. Al- though this approach is completely unrealistic, it does not negate the results of the studies. Complete knowledge of reactions for a homogeneous soil will provide a basis for solving problems dealing with layered soils. Interactions of importance will probably occur, but they should not present unsurmountable obstacles. The approaches discussed in this chapter do not represent any final solution of the problems that are posed. The approaches, however, do represent those that have been utilized and those that may contribute to the development of a successful mechanics of tillage tools. 4.2 The Reaction of Soil to Tillage Tools The reaction of soil to a tillage tool can be quantitatively described only by a mechanics. Visualize the soil as a continuous semi-infini- tive mass composed of air, water, and solids arranged in some homogeneous manner. As a tool advances in the soil, the soil reacts to the tool and some action occurs. For example, the soil may move as a mass, tlie solids may displace the air or water, or the solids may 117 118 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE break apart. The action of the soil's response can be described by such qualitative terms as plowing, cultivating, and harrowing. When a quantitative description is desired, however, numbers must replace the qualitative terms. In chapters 2 and 3, the concepts of behavior equations and dynamic properties were discussed. The behavior equations were shown to quantitatively describe simple reactions of the soil to forces and also to define dynamic parameters that assess the soil. Thus, if an action such as plowing can be represented by the simultaneous occurrence of phenomena represented by behavior equations, a possible means is available for developing the desired quantitative description. Incorporating behavior equations into a system of equations that describes an action for a specific set of circumstances is one way to develop a mechanics. The equations of the mechanics will provide the desired quantitative description. Developing a mecnanics based on behavior equations is neither new in concept nor unique to soil dynamics. The procedures are generalizations of basic principles that have evolved over the years from scientific investigations. Combining behavior equations may seem to be an easy task. In principle this is the case, but in practice complications often arise that are not apparent from the behavior equations themselves. To illustrate some of the complications, as well as the principles for developing a mechanics based on the behavior equations, examples from Newtonian mechanics will be discussed. 4.2.1 Principles for Developing a Mechanics Newton's Second Law of Motion is a behavior equation. Consider a ball that is dropped. Gravity acts on the ball and it falls. The behavior is clearly observed, and Newton's Second Law is easily identified as bein^ involved. The force of gravity is the input to the behavior equation, and movement is the output. The equation of the Law defines the behavior, and mass is the behavior parameter that characterizes the material (the ball). Thus, the Second Law is a behavior equation. Newton's Second Law does not describe the action of a falling body. Neither the magnitude of the force acting on a falling ball nor the magnitude of its acceleration is of direct interest. Kather, the action of the body is of interest and factors such as time, distance, and velocity describe the action. These factors are not directly given in Newton's Second Law. To describe the action, a mechanics is required; and the mechanics is embodied in the classical laws of falling bodies. The equations representing the laws are easily developed. Defining the mass of a body and its state (such as position and initial velocity), together with the equations defining velocity and acceleration and the equation of Newton's Second Law, provides a system of equations whose simultaneous solution yields the laws of falling bodies. The laws are a mechanics based on a behavior equation, and the laws accurately describe the action of a falling body. In this instance, a mechanics was required because the action to be described was not completely represented by the behavior equation. But this is not always the case—for example, when Ohm's Law is used to describe SOIL DYNAMICS IN TILLAGE AND TíÍACTION 119 the flow of an electric current. The inputs and outputs of Ohm's Law are directly the factors of interest so that the action is completely described. In general, however, actions are not so simple and a mechanics is required to completely describe the actions. Other principles for developing a mechanics can be illustrated by considering a spinning projectile moving through the air. Two behaviors are involved. The first is falling body behavior and the second is spinning behavior. Spinning behavior involves a force system (a couple) that acts as a behavior input, and the resulting rotating motion is the behavior output. Newtonian principles provide the basic behavior equation. The equation states that the total applied moment (couple) is equal to the time rate of change of angular momentum. The concept of angular momentum involves a behavior property called moment of inertia. The physical significance of moment of inertia is the magnitude and distribution of mass within a body. Specifying the moment of inertia of a rigid body requires six numbers so that six parameters define the behavior property (moment of inertia). Rigid body rotation about itself can be considered the basic behavior equation together with such associated definitions as moment of inertia, angular momentum, couples, and positions. Simultaneous solution of this system of equations provides a mechanics to describe the action of spinning. Indeed, the actions of gyroscopes are explained by this mechanics. Our interest in an action can dictate the nature of a required mechanics. If our interest in the spinning projectile concerns only where it will hit when it returns to the earth, falling body mechanics will be adequate. The spinning action can probably be ignored. On the other hand, if we are interested only in describing the movement of the projectile rotating about itself, falling body mechanics can probably be ignored and the spin mechanics will be adequate. If the action to be described is the path of motion of every mathematical point of the body, then both behaviors must be considered simultaneously. A mechanics can be developed to describe such an action. Simultaneous consideration of both behavior equations, together with the associated definitions of moment of inertia, velocity, position, etc., provides a system of equations to describe the action. Our interest in an action, therefore, influences how the required mechanics will be developed. Interaction may influence how a mechanics is developed. If interactions occur between behaviors, each behavior may have to be included even if our interest in the action does not require a complete description. Consider the situation where the path of motion of the center of mass of an elastic spinning projectile is the action to be described. The forces within the spinning projectile may cause movement within the body, and a shift in the mass may occur. The shift in mass will change the moment of inertia which, in turn, will change the spin action. If the change in spin is great enough, the path of motion of center of mass may be changed. All three behaviors, therefore, may need to be included in the mechanics to accurately describe the path of motion. The third behavior equation is, of course, stress-strain behavior where stresses are inputs and strains are outputs. For idealized elastic behavior, the theory of elasticity provides behavior equations ; 120 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE and bulk modulus and shear modulus are behavior parameters defined by the equations that characterize the material. Simultaneous consideration of the three behavior equations (note that stress-strain behavior is simple even though the equations are mathematically complex), together with all of the associated boundary conditions, provides a basis for a mechanics. The solution of the system of equations will account for the possible interaction. Interactions can, therefore, influence the procedure for developing a mechanics. Certain generalizations for developing a mechanics based on behavior equations can be concluded from the discussion of the New- tonian examples and can be summarized under three points: (1) The action to be quantitatively described must be defined. (2) The behavior involved in the action to be described must be recognized. (3) In most circumstances the behavior must be incorporated into a mechanics that describes the action. Point 2—recognizing the behavior involved—is by far the most difficult of the three points, because recognition usually implies selection. Defining the action, however, must be accomplished first, so it is discussed first. The action to be described is defined by interest from outside the action. A problem to be solved, curiosity, or merely a quest for knowledge are sources of interest. In the example of the projectile, interest determines whether the path of motion of each mathematical point of the projectile must be described or whether only the path of motion of the center of mass must be described. No set procedure can be established for defining an action because the procedure usually embodies simply defining the problem. Personal interest and the nature of the action itself will influence thé definition. Until the action (defined here as the doing of something) has been at least qualitatively defined, however, the problem of quantitatively describing the action cannot be undertaken. In any action known to man today, more than one behavior is involved. Behavior is defined here as any phenomenon that can be identified, isolated, and studied so that a behavior equation can be written to quantitatively describe the phenomenon. Thus, Ohm's Law, stress-strain equations, and Newton's Second Law of Motion are examples of behavior in the sense defined here. We know from available knowledge that a rigid body is not really rigid. Strain always occurs so that the concept of rigidity is relative. Similarly, a body that strains and is assumed to be continuous is really not continuous. The body is built up of crystals or aggregates formed from molecules that are, in turn, formed from atoms. When the action to be described concerns so-called rigid body movements, all of the smaller behaviors (smaller because of the physical size of their sphere of influence) can usually be ignored. Even when the action to be described is in the realm of the atomic dimensions, today we know that the atom has a nucleus and the nucleus itself is being subdivided. Presumably, behavior equations must exist for particles within the nucleus; therefore, any action known today probably involves more than one behavior. No unique system or structure of behavior equations exists. Such a structure can be developed only when matter itself can be absolutely defined. If, for example, the makeup of the nucleus itself were precisely determined, matter could perhaps be absolutely de- SOIL DYNAMICS IN TILLAGE AND TRACTION 121 fined. Even if such a structure did exist, its practicality would be limited. The practical limitation was clearly stated by Dirac, who is one of the founders of quantum mechanics ( ü^ ). Quantum mechanics deals with the motions of electrons or nuclei inside atoms and molecules. The sphere of inñuence of the mechanics is thus small. Dirac, as quoted by Eliezer, stated : "The general theory of quantum mechanics is now almost complete .... the underlying laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact solution of these laws leads to equations much too complicated to be soluble." Because no unique structure exists, because of the mathematical complexity of the structure, and because more than one behavior is always involved, two guidelines for choosing behavior involved in an action are indicated. First, the choice of behavior must be arbitrary. In other words, for any specific action most of the behavior can be ignored. Second, the mathematical complexity suggests choosing behavior where the inputs and outputs of the behavior equation are as close as possible to the factors that will describe the action. For example, stress and strain do not lend themselves to describing the path of motion of a projectile. Within these two guidelines several qualifications must be included. Only one behavior equation may be required to determine an accurate description of the action. If an interaction exists, however, an accurate description will require additional behavior equations. The added behavior equations may be very remote from factors that describe the action; if they are, the second guideline must be amended. The elastic spinning projectile illustrates such a situation. Sacrificing accuracy of the description of the action, however, may permit ignoring the interaction. The arbitrariness of the behavior structure, the requirement of mathematical simplicity, and the possibility of interaction—all indicate that judgment, ingenuity, and perhaps some luck are needed when choosing behavior to describe an action. Incorporating behavior into a mechanics is the final generalization in procedures for developing a mechanics. If the action to be described can be closely represented by a behavior equation, no mechanics is required. Ohm's Law completely represents the action of current flowing through a simple conductor. If, however, a network of conductors is constructed, a mechanics is required to describe the action of the network. But the fundamental behavior of the network itself and every element in the network is represented by Ohm's Law. As simple an action as a falling body requires a mechanics so that even when only one behavior equation is required, a mechanics must often be developed. When more than one behavior equation is required, a mechanics is required to combine the behavior equations. Just as no specific procedure can be given for defining an action, so no specific procedures can be given for combining behavior equations. Each situation has its own peculiarities. As suggested in the example of the projectile, including a second behavior equation may so change the result of the mechanics that little similarity remains. While the details of procedure will vary, combining behavior equations 122 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE usually involves considering the equations simultaneously with boundary conditions. Simultaneous solution of the system of equations results in the desired mechanics. 4.2.2 The Complete Soil-Tillage Tool Mechanics By following the principles discussed in section 4.2.1, a soil- tillage tool mechanics can be developed in progressive stages (fig. 76). The purpose of the mechanics is to quantitatively describe the action of tillage on the soil. In the initial recognition phase, the action is observed and noted to be repetitive. The recognition phase is gradually supplanted by a qualitative phase, in which the general forces are identified and specific reactions are observed. Nearly all of the world's literature on tillage research falls into the qualitative phase as defined here. The tool size and shape, width and depth of operation, speed of operation, and soil conditions are varied and the soil reaction is noted. The procedure involves trial-and-error methods of solving problems. The qualitative phase has been habit- ually utilized for problem-solving purposes; unfortunately, relations based on trial-and-error results rarely explain the underlying basic principles. Hence, the relations generally may not be used to

~~SOIL CONDITIONS AND FORCES~~

~~Soil Behaviors f:UJmmm.^mM Separated~~

~~Repetitive Soil Behavior Development of Phenomenon Recognized Observed Individual Soil Behavior Mechanics Equations Developed~~

~~Soil Behavior Equations Combined~~

~~NEW SOIL CONDITIONS~~

~~TILLAGE ACTION GENERAL WORD SPECIFIC WORD • • • • NUMERICAL DESCRIPTIONS~~

FIGURE 76.—Phases in the development of a soü-tiUage tool mechanics to to describe a tillage action. SOIL DYNAMICS IN TILLAGE AND TRACTION 123 satisfactorily explain new and untried situations, and more trial- and-error studies must be made. A soil-tillage tool mechanics must be based on quantitative descriptions of the forces applied by the tool and the resulting physical behavior of the soil. The quantitative phase in figure 76 constitutes the bulk of the basic work in soil dynamics. The actions recognized as being present in tillage must be separated into simple behavior, which can be studied. Simple behaviors include, for example, stress-strain relations, soil-metal friction, and yield by shear. Descriptions of simple behavior can be established through the application of several distinct phases of study (sees. 3.1 and 3.2). First, some specific behavior is observed and studied. Second, haying noted the behavior, factors involved in the behavior are identified and their relation is ascertained in a cause-and-effect manner. Mathematical equations are required to quantitatively describe the cause-and-effect relation and, hence, the behavior. Resorting to mathematical equations is possible only when both input and output quantities can be expressed in some form of numerical description. Each behavior equation defines a dynamic property, and the parameters of the behavior equation identify the specific quantities that must be measured. When measured values of the parameters are substituted into the behavior eq[uation, they assess the property numerically in that they quantitatively describe the material's contribution to the behavior. ^ While these steps may appear to be so elementary as to be obvious, they are not always easy to execute. Even with simple behavior, attempts to quantize relations have been extremely difficult. This difficulty is compounded since the results of behavior (the action), rather than the behavior itself, are of practical interest. Neverthe- less, behavior equations must be developed and they must be accurate and have clearly defined inputs and outputs. An axiom to use in developing a soil-tillage tool mechanics is the principle of compatibility, which can be stated: Quantities to be considered simultaneously in representing a phenomenon should have compatible levels of definition. This is to say that the definition of forces and movements used in a mechanics must be as completely defined as the inputs and outputs of the soil behavior equations which provide the framework of the mechanics. The utilization of this principle will serve to prevent the excessive development of unnecessary subbehavior equations along with their complexities. With accurate behavior equations, a complete soil-tillage tool mechanics can be developed to quantitatively describe tillage actions. A specific tillage tool has a fixed geometrical shape that can be expressed by appropriate mathematical equations. An overall coordinate framework can be established in which the direction of travel and path of motion of the tool, orientation of the tool, and the continuous nature and profile of the soil can be described. Since the tool operates as a rigid body having a much greater strength than the soil, its movement displaces soil. Describing the path of motion of the tool in the reference framework thus provides the necessary boundary conditions to define the problem. Simultaneous solution of the system of equations, utilizing the boundary conditions and the magnitude of the parameters, provides a quantitative description 124 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE of the reaction. Stresses acting on the tool can be added vectorially to give the forces required to move the tool in the specified path. The path of movement of the soil determines its total displacement and final position. Thus, from the description of the tillage action the factors of interest can be calculated. Few behavior equations have been determined that are suitable for use in a soil-tool mechanics, and a quantitative assessment cannot always be made of those that are available. Thus, the complete mechanics does not exist today, and it is not likely to be forthcoming in the immediate future. The complexity of mathematically solving the system of equations will also be a deterrent to securing a rapid solution, but a vast realm of mathematical knowledge is available for assistance. Many mathematical techniques have yet to be used in developing the mechanics. They range from methods for obtaining rigorous solutions, to approximation solutions by finite differences, to simulation on electronic analog computers. It is not lack of application of these techniques that is limiting progress ; rather, it is lack of fundamental equations expressing behaviors. Any real progress in sight lies in the development of simplified descriptions of behavior rather than in a simplified mathematical method for solving the system of equations. Thus, although the main challenge in soil dynamics research still lies ahead, the course of research to be followed is clearly defined. Based on present knowledge, the course can be charted with a reasonable degree of certainty so that at least partial success is assured. Thus, the ultimate goal of soil dynamics research is directed toward developing an extremely complex mechanics. ISTevertheless, the mechanics must be developed if we are tg reduce tillage of the soil, one of man's oldest continuing tasks, to a science. Only the most rudimentary form of mechanics has evolved and the complete mechanics needs to be developed. One has only to compare the suggestions Jenkin made in 1932 ( 201 ) concerning the development of a soil-tillage tool mechanics with the tillage research undertaken in 1964 to realize that a third of a century has slipped by without progress being made. Unless some positive attempt is made to pursue the scientific aspects of soil dynamics and concentrate on the fundamentals of soil behavior, other years will pass without progress. One of civilized man's responsibilities is to develop knowledge of this type. Any knowledge that permits man to know how his environment will act or react will enable him to become less subject to the uncertainties that have slowed his progress. The ideal soil-tillage tool mechanics that has been described here is termed complete because presumably all of the simple behaviors that may have an influence on the action are included in the overall mechanics. One of the difficulties in understanding a soil-tillage tool action is that every behavior is not always operative. A behavior may appear intermittently, and its presence may be difficult to detect or assess. For example, a dry cemented soil does not simultaneously exhibit plastic flow behavior or even compression failure to any great extent. Similarly, a wet saturated soil may exhibit great plastic flow but again little compression failure. The complete mechanics should SOIL DYNAMICS IN TILLAGE AND TRACTION 125 be capable of representing these complexities by mathematically choosing which behaviors actually occur. A mechanics can be based on a single behavior equation, however, so that a so-called partial mechanics can be developed in lieu of a complete mechanics. The partial mechanics must be restricted to situations where the incorporated behavior occurs. Several attempts have been made to develop partial mechanics where a pressing need existed to obtain solutions to specific problems in soil dynamics. While expediency dictates that partial mechanics be sought, the development is also justified because of the progress that has been made in recognizing soil reactions that are distinctly different. The general nature of such observations is indicated in reports by Nichols and Eeed ( 323 ) and by Pollard {338), As an example, average soil in a "good plowing condition" shears in a regular pattern along primary and secondary surfaces as failure occurs in the soil. The soil is usually firm and without excessive amounts of roots and stones. Dry cemented soils, on the other hand, break up into large irregular blocks whose dimensions can be controlled to some extent by the size of cut of the tillage tool. Freshly plowed or loose soils cannot be satisfactorily replowed because they lack the rigidity required to hold together so as to slide over the plow surface in a uniform slice. The soil tends to roll and be pushed by the plow. Clearly, these observations lack the definition required for any mathematical treatment. The observations do indicate, however, that in some instances a reasonably simple but repetitive behavior is involved in the reaction of soil to a tillage tool. Therefore, partial soil-tool mechanics can logically be developed and they will probably have a practical application. Indeed, only partial mechanics will be available until the complete mechanics is eventually developed. 4.3 Mechanics of Simple Reactions The distinction between a complete soil-tillage tool mechanics and a partial soil-tillage tool mechanics was made in section 4.2.2. In general, a mechanics based on one, two, or any number of behavior equations can be developed. Depending on the basis chosen, the various mechanics may not resemble each other and may even identify completely different factors. Such a situation is possible because no practical unique structure exists for building a mechanics based on fundamental behavior equations. Eecognizing this fact is essential if any mechanics is to be properly understood. The only justification for any mechanics, including the Newtonian mechanics, IS that it properly and accurately describes actions in quantitative terms. Partial mechanics as used here thus applies to any soil-tillage-tool mechanics that does not include all known behaviors. The tillage action is assumed to be composed of certain recognized behaviors and a mechanics is based on the chosen behaviors. Such a mechanics will be accurate if it truly represents the situation and is not applied to situations where the assumed behaviors do not occur. Of course, some knowledge is required to follow such procedures. As an extreme example, use of both electrical resistance behavior 126 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE and strength behavior as a basis for a mechanics to describe the flexibility of a fishing pole is unnecessary since both are not expected to be operative. Similarly, a mechanics need not include plastic flow behavior of soil if the mechanics is to be applied only to dry cemented soil. Available knowledge qualitatively indicates that plastic flow does not occur in dry cemented soils. A partial mechanics can thus be both valid and useful if its limitations are known. A final point concerning the distinction between a partial and a complete mechanics is the mathematical complexity of the mechanics. Nothing indicates nor assures that the mathematics of a partial mechanics will be simple. The principal distinction as used here is that the complete mechanics would be applicable to all conceivable situations where tillage tools are used to manipulate the soil. No limitations would be placed on the complete mechanics. In contrast, a partial mechanics will have restrictions. The restrictions may be on the soil condition to which it is applicable or the type of tool it represents, or both. In fact, a partial mechanics may have no practical usefulness, yet may be of value because it explains reasons for observed tillage actions. 4.3.1 Inclined Tools An inclined plane that is moved through the soil along a straight path at a slow speed might be considered a tillage tool. The reaction of the soil to the tool is relatively simple and is realistic; the tool causes failure of the soil in a manner similar to that described by Nichols and Eeed {323), The fundamental characteristic of the action IS a repeated failure of the soil by shear, which forms small blocks of soil (fig. 77).

~~l//fy7//r^:///^-///^////^/r~~

~~FIGURE 77.—Reaction of soil to a tiUage tool shaped as an inclined plane.~~

Soehne ( 398 ) analyzed the action of a simplified tool and concluded that four simple behavior equations described the tillage action: soil-metal friction, shear failure, acceleration force for each block of soil, and cutting resistance. Figure 78 shows the hypo- SOIL DYNAMICS IN TILLAGE AND TRACTION 127

FIGURE 78.—Hypothetical forces and their orientation on a segment of soil reacting to an inclined-plane tillage tool. (Soehne, Grundlagen der Land- technik ( 398 ).) thetical forces that act on the segment of soil as it reacts to the advancing tool. In essence, the behavior outputs have been specified. Locating failure surfaces specifies the orientation and location of the force inputs that cause the assumed behavior. The magnitude of the forces has not been specified. Forces CFi and fJiNi are due to soil shear and are those present at the instant incipient shear failure occurs. Forces due to soil-metal friction {iJ/No) and acceleration {B) are also present. Soehne visualized a pure resistance of the soil to being split by the cutting edge of the tool {kh). Thus, in principle, the simple behavior outputs have been specified in figure 78, and they represent the complex reaction of the soil to an inclined- plane tillage tool. By using the notation in figure 78, an equilibrium equation can be written for the forces in the horizontal direction acting on the inclined tool. The forces on the tool itself are not shown in figure 78, but they would be the forces reacting to those acting between the soil and tool and the draft. Equilibrium gives TT = TV^o sin 8 + ix'No cos Ô 4- hh, (57) where W — draft force, ^' = coeiRcient of soil-metal friction, No — normal load on the inclined tool, k — pure cutting resistance of soil per unit width, h — width of tool, 8 = lift angle of the tool. Soehne reasoned that the pure cutting resistance of the soil is small and becomes important only when stones or roots are present or the cutting edge of the tool is dull. In the absence of such situations, the cutting component of the total force might be considered negligible so that a specific resistance of the soil W* can be defined and may be indicated as 128 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE TF* = W-kb, TF* is the tool resistance without the cutting component TF* = No sin 8-i-NofJi'cos d, (58) Concentrating now on the soil segment rather than on the tool, the vertical forces can be summed and placed in equilibrium. With the notation and the relations shown in figure 78, equilibrium gives G-No (cos d- fji' sin 8) - ;V^i (cos ß- a sin ß) + (OF^ + B) sin ß - 0, ^ ^ ^ ^^ ^^^^ where G = weight of the soil segment, Ni = normal load on the forward failure surface, ß = angle of forward failure surface, fi = coefficient of internal soil friction, fi' = coefficient of soil-metal friction, Fi = area of forward shear failure surface, O = cohesion of soil, B = acceleration force of the soil, 8 = lift angle of the tool. The horizontal forces on the soil segment can be summed and placed m equilibrium from the relations shown in figure 78 to give No (sin8 + /A^cos8) - Ni (sinyS +/.c cos^) - (OF^ + B) cos^ = 0. (60) Equations 58, 59, and 60 can be used to eliminate the normal forces No and N^. No can be found from equation 58 and substituted into equation 60. Kearranging terms and solving for Ni gives ¡V, = W-~ (OF,+ B) cos ß sin y8 +/x cos )ß • ^^^) Substituting for No and Ni in equation 59 gives

~~^ TTTT* COS b — uf sin 81~~

rcos^-usinßl . ^^ ^ + {CF^ + B) sinyS = 0. Lsin)ß + /xcos/3j \ ^ / H Expanding and rearranging terms gives ^y^ pQS 8 - //.^ sin 8 ^ cos /3 - /x sin ^Sl ^ OF^-hB [sin 8 + ^'cos 8 sin)8 + /xcos)8j ~ sin ß-h fjL cos ß' and by letting - ["cQS 8 - ^' sin 8 cosß- fji sin ßl [sin 8 + /x' cos 8 sin yS + /¿ cos^8 J'

B ^(smß + fjLcosß)' ^^^^ SOIL DYNAMICS IN TILLAGE AND TRACTION 129 Equation 62 relates the forces acting in the soil-tool system. In principle, the unknown forces No and Ni have been mathematically eliminated and that is all that can be accomplished by these manipulations. Since pure cutting behavior has been ignored and acceleration behavior has not yet been utilized, only two behavior equations are represented in equation 62. Thus in prmciple, the two equations have eliminated two unknowns. The remaining unknowns in equation 62 must be determined from the remaining behavior equation (acceleration) and other relations yet to be developed. Parameters of the behavior equations, of course, must be experimentally determined since they characterize the soil or metal. Other parameters will characterize the mode of operation. In a loose sense the parameters may be considered as boundary conditions. The weight of soil may be calculated from the volume of the soil supported by the inclined tool. Figure 79 shows a trapezoidal area

~~FIGURE 79.—Geometrical relations between velocities and lengths for a segment of soil reacting to an incUned tiUage tool. (Soehne, Grundlagen der Landtechnik {S98).)~~

that may be assumed to be supported by the tool. The area of the trapezoid multiplied by the depth of the area (width of tool) and the density of the soil gives the weight. By using the relationships in figure 79, the weight of soil is

~~G = yM- (z. + ^^), (63)~~

~~where y = wet bulk density of soil, J =z width of tool,~~

sm jS cos (6 + ß) Li = d sin^S L2 = 6?* tan 8. 130 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE The area of shear Ft can be easily determined from either figure 78 or 79, and the area is given by "^ = itß- m The acceleration force B is the only item in equation 62 that remains to be specified. Newton's Second Law of Motion provides the behavior equation, and it can be written

~~5 = m^, (65)~~

where m = mass of the soil accelerated, V = velocity of the accelerated soil, t = time. Soehne argued that if the periodic failure process is considered to be continuous, then the total work done to bring about acceleration is not changed significantly and an average constant force can be determined. The soil can thus be visualized to be at rest; but in some time t it reaches a velocity Vs, as shown in figure 79. The mass of soil to be accelerated in time t is given from the volume of soil disturbed in time t so that

~~m = -^hdtvo, (66)~~

~~where y = wet bulk density, h = width of tool, d = depth of soil disturbed, t = time, Vo = velocity of the tool, g = acceleration due to gravity. Soehne assumed that~~

dt "= At ~ t-0 ~ T (^'^^ since the soil was initially at rest at time t ■=^ O, In addition, the magnitudes of the velocity vectors were considered to be so related that they form a closed triangle. Thus, from figure 79

~~Vo — 'Z^s COS )8 + ^e COS 8, and Vs sin ß = Ve sin S, so that Ve can be eliminated to give sin 8~~

~~Substituting equations 66, 67, and 68 into equation 65 and simplifying gives ^ "'~~

p — B = ^g Mv-^ " -r#^.sin (8 + ^) • (69) SOIL DYNAMICS IN TILLAGE AND TRACTION 131 Equations 63, 64, and 69 could be substituted into equation 62 to provide a single equation in which parameters of the tool, soil, and mode of operation are related to the horizontal force to move the tool. Thus, tool parameters h and Z», soil parameters ja, y, and (7, soil-tool parameter /x', and mode of operation parameters d^ Vo and ô provide the basis to describe the tillage action. Soehne did not indicate how he determined the value for ß. The angle can be calculated from the relations shown in figure 41. Equations 17 and 18 define the relations ¡ji = tan (j) where (^ is the angle of internal friction. Figure 41 shows that the shear surface will be oriented 90° - <^ from the largest principal stress. By following the usual sign conventions and recalling that the magnitude of angles in the Mohr's circle represents twice the magnitude of the angle in the physical body, ß can be evaluated from the equation ^ = i/2(90°-(^). (70) Vertical forces on the tool could be placed in equilibrium to provide a relation similar to equation 57 and equations 59 and 60 again could be used to calculate an equation similar to equation 62. Equation 62 and its implied vertical counterpart thus constitute a simple mechanics for inclined tools. Soehne attempted to verify equation 62 experimentally. He did not use the soil and tool arrangement shown in figure 77, which eliminated extraneous forces ; he used a similarly inclined tool that was supported only in the center. Because it was operated entirely below the surface of the soil, some forces on the edges of the tool and on the supporting standard were not considered in the mechanics. Figure 80 compares the measured and calculated values. Additional values not shown in figure 80 were measured for a loam soil and were found to be approximately 18 percent lower than values calculated by the mechanics. The lack of agreement indicates that the mechanics is not completely accurate. On the other hand, the values are close enough to indicate that the mechanics is not completely wrong. Any one of several factors could contribute to the lack of agreement. First, edge and supporting standard effects were present for the tool, but not for the mathematical model. Second, experimental determination of the dynamic soil parameters may have been in error for reasons discussed in section 3.2.1.1. Third, the behavior equations may not have been properly applied. Soehne assumed that No and Ni were constant along the respective surfaces on which they act. Dis- tributions are not necessarily uniform. In fact, moving pictures of such failures indicate that the shear failure surface may be a progressive failure rather than a simultaneous failing of the entire surface. The velocity imparted to the soil that caused acceleration was assumed to be Vs^ No justification can be put forth to assure that the assumption is valid. Furthermore, the concept of an average acceleration may not describe the situation. Needless to say, if all of the points concerning possible misapplication of the behavior equa- 132 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~28r~~

~~24 24 d = 20 cm. 20 • MEASURED VALUES 'S^ 5 20~~

~~ILÜ ÜJ 16 Ü Ü Z 16~~

~~-j -L. 5 10 15 20 10 20 30 40~~

~~FURROW DEPTH (cm) CUTTING ANGLE (»)~~

~~(A) (B)~~

~~FIGURE 80.—Soil resistances (draft) are measured and calculated for an inclined tillage tool operating in a sandy soil. ( Soehne, Grundlagen der Land- technik (398).)~~

tions were included, the mathematics would-be greatly complicated. Fourth, pure cutting was assumed to be negligible. Fifth, the behavior equations themselves may not be accurate, even though they represent real phenomena. Kefinement in any one of these limiting factors could greatly improve the accuracy of the mechanics. Also, the mechanics has not been experimentally checked over a wide enough range of variables such as speed, depth, soils, and cutting angles to establish the accuracy of the mechanics. Additional verification is needed. Kowe and Barnes ( 875, 376 ) attempted to overcome some of the inherent limitations in the mechanics. They used the physical arrangement shown in figure 77 to eliminate the influence of extraneous forces along the sides of the soil block and the standard holding the tool. They also incorporated into the mechanics the influence of adhesion on the soil-metal sliding surface. The adhesion parameter Oa (sec. 3.2.1.6) requires a change in the forces shown in figure 78. The change is shown in figure 81. Incorporating the adhesion parameter changes equation 62 to give

G GF^-VB GJTQ TF* + + ■ (71) z B (sin ß-{- fjL cos ß) ^(sin8 + />t'cos8) ' where Fo = area of inclined tool, Ga = soil-metal adhesion. Rowe and Barnes were primarily concerned with the influence of speed on the magnitude of the soil shear parameters, which would, in SOIL DYN"AMICS IN TILLAGE AND TRACTION 133

FIGURE 81.—Free body diagram showing sliding force components due to friction and adhesion. (Rowe and Barnes, Amer. Soc. Agr. Engin. Trans. ( 376 ).) turn, influence the draft. Consequently, they measured the soil shear parameters at various speeds and assumed that the soil sheared at velocity Vs^ which can be calculated by equation 68. The results of their measurements and calculations are shown in figure 82. A reasonable agreement was obtained between calculated and measured values, but it appears that equation 71 has not been satisfactorily verified. Since Rowe and Barnes used only one tool orientation and one depth of operation, the data should probably be considered as a check on the mechanics as developed by Soehne rather than as a special study on the effect of speed. Regardless of how the data are

~~SILTY CLAY LOAM CALCULATED MEASURED~~

~~SAND CALCULATED MEASURED~~

~~0.5 1.0 1.5 2.0 2.5 TOOL VELOCITY (Ft./Sec.)~~

FIGURE 82.—Measured and calculated draft of an inclined tillage tool at various tool velocities. (Rowe and Barnes, Amer. Soc. Agr. Engin. Trans. ( 376 ).) 134 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE viewed, however, considerable improvement is required before the mechanics will be accurate. Kawamura ( 207, 212 ) followed a different approach in developing a mechanics of inclined tools. His work actually preceded that ot hoehne but, unfortunately, delay in translating his work has limited Its availability. Kawamura ( 209 ) measured the draft force ot an inclined tool when it was operating at various depths and hit angles (angles of inclination). The measured results show (fig. 83) that a minimum in draft force occurred at a lift angle of about

~~E Û-~~

~~FiGURE 83.—The effect of depth of cut d and lift angle ô on the draft force of an inclined tool. (Kawamura, Soc. Agr. Mach. Jour. (Japan) ( 2ÖP ).)~~

25° for shallow operating depths; at deeper operating depths, the minimum m draft force shifted to a lift angle of about 15°. An interesting point is that Soehne's calculated curves (fig. 80) have the same shape as the experimentally determined curves shown in figure 83, so that Kawamura's data tend to confirm the curves calculated from Soehne's mechanics. One difference in the experimental procedure was that Soehne changed the length of his tool so that the lift height was constant with various lift angles. Kawa- mura, on the other hand, maintained a constant length of tool so that the lift height was varied with the lift angle. Another difference was that Kawamura's data were obtained at very slow speeds, whereas Soehne used a speed of 1 meter per second which is approximately 21/4 miles per hour. While not expressly stated, Kawamura apparently used speeds only one-tenth as fast as those of Soehne. Kawamura also investigated the shape of the shear failure surfaces that resulted in separation of the blocks of soil. When forward velocities of the tool were very slow, the detached blocks of soil remained intact. As a result, the shape of the shear surface and the angle between the shear surface and the soil surface could be measured. The shear surfaces were observed to be curves rather than SOIL DYNAMICS IN TILLAGE AND TRACTION 135 straight lines, and on occasion the curved shear surface extended slightly below the lowest part of the tool. Kawamura also noted that at increased forward velocities of the tool, the angle of the shear surface tended to alternate about two relatively constant values. The extreme values of the angles occurred (1) when failure started at the tip of the tool and went upward, and (2) when failure started at the tip of the tool and swept downward, then upward. Because of the curved surface and the al- ternating angles, a mean shear angle ß was used (fig. 84). Figure

~~FIGURE 84.—Measurement of the angle of a shear surface for a sou reacting to an inclined tool. (Kawamura, Soc. Agr. Mach. Jour. (Japan) (209).)~~

84 also shows a clever means that was used to determine the average shear angle experimentally. Kawamura noted that as the tool approached the location of the Ames dial, the surface of the soil rose linearly (slope ^ 0.001-0.01) with the advancing tool until a critical range was reached. During the critical range the surface rose at an increasing rate as the tool continued to advance (relation was a curve). After the critical transition range had been passed, the relation between the rising surface of the soil and the advancing tool was again linear but at a much higher rate (slope ^/ 1.5) than before the critical range. Kawamura believed that the last linear movement was due to the rigid block of soil rising on the inclined tool, whereas the initial linear movement was due to the elastic behavior of the soil. The critical range, however, coincided with the formation of the shear surface and reñected the transition state between the time when the block of soil was part of the soil mass and when it was completely separated from the soil mass. The shear surface could thus be approximated by a straight line extending from the tip of the tool to the soil surface where the critical range began. The average angle of the shear surface could be determined from the relation tan ß = -y-,

with values obtained from figure 84. In other aspects of the work, the lift angle of the tool was observed to influence the mean shear angle so that the shear angle was not a constant for a given soil condition. Figure 85 shows the measured relation for two depths of tool operation. The data indi- 136 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~_ 30~~

~~10 10 20 30 40 50 8 n~~

FIGURE 85.—The relation between the lift angle (5) and the average shear surface angle (ß) for soil reacting to an inclined tool. (Kawamura, Soc. Agr. Mach. Jour. (Japan) ( 209 ).) cate that the average shear angle is influenced by both the depth of tool operation and the lift angle of the tool. Kawamura used two theories from the so-called classical soil mechanics in attempting to calculate the draft force. Both theories are based on one behavior equation—yield by shear as represented by equation 18. In the Kankine theory, the shear angle is a constant given by equation 70. By considering only the mass of the soil and the shear failure stress (ignoring the magnitude of the normal stress), the weight of soil and total shear stress on the failure surface can be calculated. Equilibrium conditions then permit determining the draft component. In the Coulomb theory, the same procedure is followed except the shear angle is given by a complicated relation involving the lift angle and the soil friction angle. Neither theory, however, was sufficiently accurate to be acceptable. Since the observed shear surface was a curve and the angle of the shear surface varied with the tool lift angle, Kawamura ( 210 ) attempted to use plastic equilibrium to calculate the observed phenomenon. He reasoned that the inclined tool often created a stress state in the soil different from that required for applying either the Coulomb or the Eankine theories. He envisioned a transient region between the tool and the conditions that were accurately represented by the Coulomb or Eankine theories. At large lift angles, the Coulomb theory predicted the measured draft closely but the Eankine theory predicted the observed shear angle better than did the Coulomb theory. Thus, when small lift angles were used, the deviations between measured and calculated draft could be attributed to the transient stress region. If the transient region could be considered to be in a state of plastic equilibrium, the condition could be properly described by using available plastic flow theories. The mathematical details for using plastic flow theory are too long and too complex to be presented here. A discussion of the principles, however, will illustrate the procedure Kawamura used to develop a mechanics. When all displacement lies in a plane in a stress-strain situation, state of plane strain is said to exist. Such a situation occurs for a wide inclined tool, since all displacement can SOIL DYNAMICS IN TILLAGE AND TRACTION 137 be assumed to lie in a plane containing the direction of travel and a direction normal to the surface of the soil. If the soil material is assumed to be incompressible, one can demonstrate that there always will exist two directions (oriented at right angles to each other and normally identified as a and ß) that bisect the principal directions of strain (normally identified as directions 1 and 2). Directions a and ß are characterized by vanishing linear strain and have maximum angular or shear strain. The curves that are every- where tangential to these directions form two families of orthogonal curves that are often termed ''slip lines." Since all movement on such lines is tangential (slip), the name is appropriate. The formation of slip lines in a physical material represents a transient state of incipient failure. Before a state of incipient failure occurs, an infinitesimal increase in the stresses results in an infinitesimal increase in strain. When the stresses are in a state of incipient failure, however, an infinitesimal increase in the stresses results in a large increase in strain—this is, plastic flow. For a perfectly plastic material, the stresses causing failure cannot be increased beyond the incipient failure state since failure is reached and the material will flow plastically to adjust to boundary conditions. As one might suspect, the direction of plastic flow is parallel to the slip surfaces. Thus, the stress state at incipient plastic flow represents a condition of plastic equilibrium in the material. Specifying the criterion for plastic flow requires a behavior equation that in turn makes possible the establishment of a mechanics. By referring the stresses to a coordinate axis oriented along the slip lines and by using the differential equations of equilibrium on stresses, a two-dimensional plastic flow theory can be developed. Solution of the equilibrium equations, together with the yield criterion and appropriate boundary conditions, determines the magnitudes of the stresses and the equations of the slip lines. However, the solution is not easily obtained except in simple circumstances. Nothing in the theory describes reactions either before or after incipient failure. Hence, the solution is valid regardless of any stress-strain relations before incipient plastic flow. In order to assure that the slip lines are orthogonal families of curves, however, the material must be incompressible and displacements must lie in one plane. All these situations do not have to exist in order to have slip lines formed; but when the slip lines are not orthogonal, their description becomes very complex. Kawamura used the general procedures of plastic equilibrium in developing a mechanics. For the yield criterion he used shear failure as given by equation 18; this is the only behavior equation in the mechanics. Because of the nature of boundary configurations for the inclined tool, he used polar coordinates as shown in figure 86. He obtained expressions for the equilibrium equations in the chosen coordinate system and in terms of the shear yield condition. From boundary conditions and considerable mathematical analysis, Kawa- mura was able to demonstrate that angle ß' in figure 86 could be reasonably assumed to be independent of the fadius coordinate and a function only of the angular coordinate. Such an assumption simplified the equilibrium equations, and a numerical solution of the equations could be obtained. The diíRculty in obtaining an analytical 138 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

/m'^7/m//r7wwmmmr- FiGURE 86.—Polar coordinates used to represent stresses on a slip line caused by an inclined tool, ß' is the angle between the radial direction and the ?'^fn^\ ^^^ ®^^^ ^^°^- (I^awamura, Soc. Agr. Mach. Jour. (Japan)

solution resulted from the complexity of the mathematics but not from the complexity of the physical principles. With a numerical solution obtainable, Kawamura summed the tangential stresses on the slip surface and equated the horizontal component to draft. Figure 87 shows a comparison of experimental

~~24 r~~

~~CALCULATED- 20~~

~~^< 16 Û 14~~

~~12-~~

~~10 10 20 30 40 50 S {")~~

~~FIGURE 87.—Calculated and experimental draft values for an inclined tiUage tool. (Kawamura, Soc. Agr. Mach. Jour. (Japan) (210).)~~

and calculated draft values over a range of lift angles. The agreement is reasonably good, but more data are required to verify the procedures. Eecall that Kawamura has not considered soil-metal friction or acceleration forces, and their consideration might improve the accuracy of the mechanics. On the other hand, he has recognized and considered the curved failure surface and the possibility of a varying stress distribution on the failure surface. Kawamura concluded that his procedures represented and explained observed facts better than any theories that were available at that time. While his procedures are mathematically complex (primarily because of permitting a nonconstant stress distribution), they do represent a mechanics for inclined tools. SOIL DYNAMICS IN TILLAGE AND TRACTION 139 4.3.2 Vertical Tools A vertical plane, perpendicular to the direction of travel, represents a simple form of tillage tool. Payne ( 329 ) studied tools of this type in detail. Based primarily on the passive earth pressure theory of Rankine, Payne was able to develop a mechanics to represent the tillage action. He began his study by qualitatively observing the soil reacting to a vertical tool. Figure 88 shows the observed soil failure.

~~(A) (B)~~

~~FIGURE 88.—The nature of soil failure caused by a vertical tool in a firm soil : A, Side view; B, plan view. (Payne, Jour. Agr. Engin. Res. ( S29 ).)~~

For wide tools, the side effect can reasonably be ignored since their area is small compared to the bottom failure surface (fig. 88). A tool was considered to be a wide tool when its width was at least twice its depth of operation. The classical Rankine theory can be modified to represent the curved failure surface shown in figure 88, A, When friction is present between the soil and the tool, the directions of principal stresses do not remain horizontal and vertical. At the surface of the soil, the principal stresses must be horizontal and vertical; but their orientation rotates as one proceeds downward along the failure surface to the vertical tool. The rotation results in the curved surface. The shape of the curve has been demonstrated to be a logarithmic spiral, and methods are available to determine the stresses and the actual arc of the logarithmic spiral ( 4^7 ). Payne concluded that the modified Rankine theory represented wide tools with reasonable accuracy. When narrow tools are considered, side effects can no longer be ignored. Furthermore, Payne reasoned that shear failure surfaces must exist which pass along the sides of the tool as well as the bottom of the tool. Such surfaces will interrupt the bottom curved failure surface shown in figure 88, -a, and these surfaces will be at Í ~7" — "^ ) to the principal stress. In narrow tools, Payne further reasoned that the vertical shear surfaces would intersect each other as well as the bottom curved surface. Thus, a wedge of soil immediately adjacent to the tool would be isolated from the rest of the soil block that was sheared from the soil mass. In wide tools, the vertical shear surfaces would not intersect each other so that the wedge would never be formed. The wedge changes the boundary conditions for the Rankine theory so that the failure zone of soil can be 140 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Visualized ^ as shown in figure 89. Payne observed the failure sections quahtively as shown in figure 89, B in various soil conditions. He argued that the foregoing analysis explained the reasons for the observed action.

~~WING~~

~~WEDGE~~

~~WING~~

~~(B)~~

~~FIGURE 89.—The nature of soil failure for soil reacting to a narrow vertical tillage tool. (Payne, Jour. Agr. Engin. Res. (52P).)~~

An additional complicating factor was that the isolated wedge did not remain stationary but moved slowly up the face of the vertical tool. Payne concluded that the curved surface on the bottom of the wedge was so inclined that the forces acting on the bottom would cause the movement. He described the formation of the sheared block of soil as follows : As a narrow tool advances, it pushes forward and upward a triangular wedge-shaped block of soil {ahcdef in fig. ^^' ^.)/ "T^® wedge, m turn, pushes sideways and upward two blocks oí soil on each side of the center line of the tool in the direction of travel. He termed the soil broken loose but not part of the wedge as the crescent. The knifelike action of the wedge causes the symmetrical formation of four blocks of soil adjacent to the wedge in the crescent (fig. 89, B), One half of the crescent is shown in figure / '^zT?,x^^^\^fAi^^^ i^s ^i^g section (bcdejk) and front section {Gdtij ). All five sections are identified in figure 89, B, With the identification of the failure zone, a basis was available on which to describe the forces acting during failure and, ultimately, to develop a mechanics. Since the wedge is the only block of soil m contact with the tool, a description of the forces on the wedge is sufficient to determine the forces on the tool. Payne used two behavior equations to describe the forces on the wedge: soil failure by shear (equation 18) ; and soil-metal friction, which included adhesion (equation 47). He used the behavior outputs to specify the nature and location of the forces acting on the wedge m the same fashion as did Soehne and Kawamura. Both behavior equations represent failure conditions; thus, his first task was to describe the shape of the wedge since the wedge was formed by the failure surfaces. The sides of the wedge {acdf and Icde in fig. 89, A) were formed by shear failure, and they were assumed to be plane and not curved. Observation of the shape and action of the wedge on a narrow vertical tool during movement confirmed the validity of the assumption. The bottom of the wedge {def in fig. SOIL DYNAMICS IN TILLAGE AND TRACTION 141 89, A) must be slightly curved; but, since such a small portion of the total curved surface is contained in the wedge, the bottom surface can be assumed to be plane. Payne defined the angle between the shear surfaces on the sides of the wedge and the direction of travel as X, and the angle between the bottom shear surface and the direction of travel as r. Eight forces (a total of 10, since the wedge has two vertical sides) were envisioned as acting on the wedge. Figure 90 shows the direc-

~~FORCES LIE IN THE PLANES PROJECTIONS LIE IN THE PLANES~~

~~DA andW~~

~~DIRECTION OF TRAVEL DIRECTION OF TRAVEL~~

~~(A) (B) HORIZONTAL VERTICAL~~

FIGURE 90.—Orientation of forces acting on soil wedge in A, horizontal plane, and B, vertical plane. (After Payne, Jour. Agr. Engin. Res. (329).) tion of the eight forces and their inclinations to various reference directions. Two forces act on the back side of the wedge (soil-tool interface, aief in fig. 89, A) : (1) an adhesion force Z>^ acts tangentially; from symmetry, it must lie in a vertical plane as shown m figure 90, B; (2) the resultant of the normal and frictional forces DR acts on the back side of the wedge. From symmetry, the force must lie in a vertical plane containing the direction of travel ; and it will be inclined to the direction of travel by the angle of soil-metal friction 8. Thus, DB is oriented as shown in figure 90, i?. . A cohesive force Be and the resultant of the normal and frictional forces BB act on the bottom surface of the wedge. The cohesive force a<;ts tangentially to the surface; and, from symmetry, it must lie m a vertical plane containing the direction of travel. BG IS shown inclined at an angle r to the direction of travel in figure 90, B, Because of symmetry, the force BR also must lie in a vertical plane containing the direction of travel. The force will make an angle (f) (angle of internal soil friction) with the normal to the surface on which it acts, so that BB is inclined {(j) + r) to the vertical direction, as shown in figure 90, B, ^ ^ ^ ^ _ . Forces similar to those on the bottom of the wedge must also act 142 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE on the sides of the wedge. Because of the relative movement between the wedge and each wing of the crescent, the orientation of the forces is not as simple as for those on the bottom of the wedge. A cohesive force Sc on the side of the wedge acts tangentially to the surface; its projection in a horizontal plane will parallel the sides of the wedge and will make an angle X with the direction of travel, as shown m figure 90, J.. Payne defined the angle between a horizontal plane and Sc as ß, so that the projection of Sc in a vertical plane containing the direction of travel will be inclined to the direction of travel as shown in figure 90, B, The resultant of the normal and frictional force SR also acts on the sides of the wedge. eJust as B^ acts at an angle ó to the normal of the surface on which it acts, so SR acts at an angle ó to the normal of the side of the wedge. Because of the upward movement of the wedge relative to the wings of the crescent, .S^^ will also be inclined at some angle to a horizontal plane just as was Sc. 1 o represent the orientation of SR, Payne defined 6 as the angle SR makes with a horizontal plane; its projection in a vertical plane containing the direction of travel will make an angle 0 with the direction ot travel, as shown in figure 90, B, In the horizontal plane, Payne denned the angle between the normal to the side of the wedge and the horizontal projection of SR as a. Thus, the projection of SR in a horizontal plane is oriented, as shown in figure 90, A, Payne envisioned a force resulting from the shear failure of the two fronts of the crescent (fig. 89, B) that acts on the leading edge ot the wedge. From symmetry, the force must lie in a vertical plane containing the direction of travel. Payne designated the torce as T and reasoned that it could be considered to act at some average angle (9„, to the direction of travel, as shown in figure 90, B, 1 he final force that Payne considered was the weight of the wedge resulting from its mass. The weight, of course, acts in a vertical direction, as shown in figure 90, B. The components of the forces acting on the wedge in horizontal and vertical planes (the latter containing the direction of travel) can be determined from figure 90, and these components are shown in of ^^^ ^ ""i ^^^ ^^ ^^^ ^^ ^^^ ^^^^ ^^^^ ^i ^^^ wedge, and figure 90, B shows that DR will have the components shown in figure 91. Be has components modified by the angle r, whereas BR has components modified by the angle (cf) + r) (fig. 90, B) ; and the respective components are located as shown in figure 91. Similarly T has components modified by the angle 6^, The vertical components ot the torces on the sides of the wedge can be seen directly from figure 90,^. Since both ß and 0 are angles between the respective torces and a horizontal plane, the vertical components will be SR sin e and Sc sm ß for the side forces SR and Sc. These components are shown m figure 91, B, Similarly, the projections of the two torces m a horizontal plane will be given by the cosine of the respective angles so that the projections of Sc and SR shown in figure 90, B have a magnitude of Sc cos ß and SR COS 0. The components of the two torces m the direction of travel can thus be determined from figure 90,^; they are SR cos 0 sin (a + r) and Sc cos ß cos X, as shown in figure 91, A, The weight of the wedge W acts only in the vertical direction, as shown in figure 91, B. SOIL DYNAMICS IN TILLAGE AND TRACTION 143

~~DIRECTION OF TRAVEL . ^~~

~~w DR Sin 8 1 t. Sin^M SRCOSÖ Sin(a+X) Sc Cos ß Cos X DRCOS 8 SpSinö ScSm)3 < T COSÖy Se Cos^ CosX 1 BcSinr S-Cosö Sln(a + X) B^ COS(<^ + T)~~

~~(A) (B) HORIZONTAL VERTICAL~~

~~FIGURE 91.—Location and direction of forces acting on a soil wedge: A, Hori- zontal plane; ß, vertical plane. (After Payne, Jour. Agr. Engin. Res. {329).)~~

The forces in figure 91 can be placed in equilibrium. From figurengure 91, A,A^ DR COS 8 = 5c cos T + BR sin (<^ + r) + T cos tfm + 2 [SR COS 0 sin (a + X) + Sc cos ß cos X]. (72) There are two vertical sides of the wedge, and the vertical forces can beUÜ placedpiaucu. inIll equilibriumcîûiiiuiiuiii sooKj thatvxíKxv from figure 91, 5, W + DR sin S-^DA-Â + BeBcSiiiT sin r = Tsin 0^. + BR COS (é(<^ + T) + ^ [/S'A sin 6 + Sc sin )8]. (73) From equilibrium of forces on the tool (not shown), DR COS 8 will be the draft. One unknown can be eliminated in a simultaneous solution of equations 72 and 73. The angles 8 and <^ are dynamic soil parameters that can be measured, but the remaining unknowns must be determined from other relations. Equations 72 and 73, however, are a basis for developing a mechanics of narrow vertical tools. The angles X and r that describe the shape of the wedge are determined by the angles of soil-metal friction and internal soil friction. Soil-metal friction acts on the back side of the wedge (soil-tool interface), since the wedge moves up the tool. The adhesive component of equation 47 is small compared to the friction component so that the principal stress acting on the back of the wedge can be assumed to act in the direction of DR, Since the principal stress is compressive, it will be algebraically the smallest principal stress; as shown in figure 42, the shear surface will be inclined \~T"^~£~) to the principal plane—a plane perpendicular to DR. Note that the shear surface will be inclined i~T~2) ^^ ^^® direction of the principal stress—the direction of DR. Thus, in figure 91, 5, 144 AGRICULTURE HA]SLDBOOK 316, U.S. DEPT. OF AGRICULTURE

where r = angle between a horizontal plane and bottom failure surface, 0 = angle of internal soil friction, 8 = angle of soil-metal friction. Similarly, in the plane in which the algebraically smallest principal stress lies (a plane containing DR that is inclined to a horizontal plane by the angle 8), the shear surfaces of the sides of the wedge must also be inclined \~T~~2) ^^ ^^^ principal stress or, as indi-

cated earlier, i^^ + -^j to the principal plane. The projection of this angle in a horizontal plane, however, is a function of the angle 8 and trigonometric relations give tanf-^-A\ tanX = \-±-^-L /75y cos 8 ' ^'^^ where X = angle between the direction of travel and sides of the wedge in a horizontal plane.

The angles X and r are indicated in figure 91. Equations 74 and 75 thus permit calculating the angles defining the shape of the wedge. The adhesion force Dj^ is easily calculated by multiplying the adhesion parameter Ca by the area over which it acts. Thus

T>A. = CJa, (76) where I = depth of operation of tool, a = width of tool, Oa = soil-metal adhesion. Similarly, the cohesive force on the bottom surface of the wedge is the product of soil cohesion and the area over which it acts. Geo- metrical relations give

~~^ 2 ^ tan X COST ^ tan X COST' ^^^^ where C — soil cohesion at failure.~~

BR was eliminated from equations 72 and 73 so that its components did not need to be determined. The cohesive force on the sides of the wedge is also a function of the area. Because of the vertical relative movement, the sides of the wedge were considered to be "old" failure surfaces so that residual cohesion {Cr) rather than failure cohesion (sec. 3.2.1.1) would be acting. From the geometry shown in figure 91, SOIL DYNAMICS IN TILLAGE AND TRACTION 145 _ Crd r, atanrl (78) ° ~ ß sin X L ~^tanxj' where I = depth of tine, a = width of tine, Cr = residual cohesion of soil. The weight of the soil wedge can be computed from its volume and is given by [atanr]atanr' W (79) ^tanX ~^tanxj' where W = total weight of wedge, 7 = wet bulk density of soil.

By eliminating BR with a simultaneous solution and by using equations 74 through 79, all terms in equations 72 and 73 are determined except the forces T and SR and the angles Ö, j3, a, and dm- These six unknowns could not be. determined directly, but Payne was able to use passive earth pressure techniques to evaluate them. The details of applying passive earth pressure theory will not be repeated here since they are lengthy and are reported in various sources, such as Terzaghi and Peck ( 4^7 ). The theory is based on one behavior equation, yield by shear, and the theory could be termed a mechanics as mechanics is defined here. Payne applied the theory to the problem by Qonsidering that a wing of the crescent (fig. 89, B) is held by the side of the wedge ; thus, the side of the wedge becomes a "retaining wall." In principle, Payne calculated the resultant passive earth pressure on the wing of the crescent and resolved it into the components acting on the wedge defined in figures 90 and 91. The resultant pressure usually cannot be determined directly, but techniques permit calculating when the pressure is a minimum. In such a state, the shape of the wing (its failure surface) and the magnitude of the desired forces can be determined. Figure 92 shows the forces acting on the wedge and their locations.

~~WING~~

~~DRCOSS cos dp ^ SR COS 6 p cos op ¡c COS)ö F cos ß~~

~~(A) (B)~~

FIGURE 92^.—Forces and their location while acting on a wedge of soil formed by a narrow vertical tool: A, Horizontal plane; B, vertical plane. (Payne, Jour. Agr. Engin. Res. {329 ).) 146 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Figure 93 shows the forces on the side of the wedge in perspective as well as on a cross section of the wing. From figure 93, J., Payne obtained four equations relating the angles and forces associated

~~SIDE OF WEDGE Sc SIN ß~~

~~(A) (B)~~

FIGURE 93.—Forces acting on the side of a wedge of soil: A, In perspective; B, on a cross section of the wing. (Payne, Jour. Agr. Engin. Res. ( 329 ).) with the sides of the wedge. Determination of the direction of the resultant of the minimum passive earth pressure on the side of the wedge by a series of trial computations specified enough values so that the four equations could be solved. The same techniques were applied to the fronts of the crescent to determine the directional angle öm and the force T, An allowance had to be made because of the shape of the fronts since they form a sector that meets at the leading edge of the wedge. The wings were assumed to have a constant width, as shown in figure 89, 5, whereas the fronts do not have a constant width. The minimum passive earth pressure for the fronts was determined ; this, in turn, specified the values for T and öm. Applying passive earth pressure theory to the wings and fronts of the crescent and including equations 74 through 79 reported here gave Payne 13 equations to use in determining the required unknowns in equations 72 and 73. The complex arrajr of equations tends to compromise his mechanics for the narrow vertical tool. The essential difference between the soil reaction description for the operation of narrow and wide vertical tools lies in the description of the wedge. For wide tools, the resultant passive earth pressure was considered to act directly on the tool; the tool is the "retaining wall." For narrow tools, however, the wedge becomes the "retaining wall" for each of the segments of the crescent. Payne carried out a series of experiments to determine the validity of his mechanics when a narrow vertical tool was used. Measure- ments were made under field conditions rather than in a laboratory where a soil bin might have provided better control of the conditions. He used four soil conditions including sandy loam, silty loam, and clay loam types. Tool widths ranging from % inch to 4 inches were used while the depth of operation was maintained approximately constant at 5 inches. As a result, a reasonably wide range of both SOIL DYNAMICS IN TILLAGE AND TRACTION 147 tool and soil parameters was used in an attempt to verify the mechanics. Equations 72 and 73 may be used to predict the draft of a narrow vertical tool at the instant of failure of the shear surfaces; hence, the predicted draft value will be a maximum. As the tool continues to advance, the draft should be at some lower value until another failure state has been built up. Numerous researchers have noted variations in measured drafts, which may be explained by a series of shear failures as the tool advances. Some measure of the variation should be taken into account. An analysis of the results showed that the draft could be assumed to be nearly proportioned to cohesion. Since Kîohesion ranged from a low of Cr to a high of È/, an estimate of the minimum draft could be calculated from the relation

where B^ax — maximum draft as determined from equations 72 and 73, Dmin — minimum draft. Payne analyzed his measured drafts in such a manner that he could determine their frequency distribution. It was then possible to construct a diagram that showed the percentage of time the draft was at a certain value. When this distribution was compared with the predicted range of draft {Bmax and D^in)^ the measured draft that fell within the predicted range varied from 6 to 78 percent. The apparent discrepancy between measured and calculated results does not completely prove or disprove the validity of the mechanics. The measured range of values was always greater than the calculated range, so that a low percentage of agreement was observed whenever the measured range was much greater than the calculated range. The measured range should have been larger because it included the random variation in the soil strength—the variation in dynamic soil parameters. The calculated range given by equation 80, however, was based on average values for C and Cr without regard to their distribution. If the largest value of C and the smallest value of Or had been used, a much larger predicted range would have resulted and the percentage of measured draft falling within the predicted range would have been much larger. To better determine the validity of the mechanics, the arithmetic mean of the predicted range of draft was compared with the mean of the measured draft as determined from the frequency distribution diagrams for all of the tools in all soil conditions (fig. 94). The correlation is highly significant, but the fitted regression is also significantly different from one. Thus, the arithmetic mean correlates with the measured mean but gives a value that is higher than the measured mean. Payne pointed out that he assumed that the true mean oJE the predicted range was equal to the arithmetic mean—that is, a normal distribution. Nothing justifies the assumption of a normal distribution so that the arithmetic mean may be higher than the true mean. This remains to be established, however, so at the present time (1965) it is considered that the arithmetic mean does 148 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~Y 95% œNFIDENCE LIMITS o 500 tr, FITTED REGRESSION- o (bxY =0.7516) / o Lu 400 fe o REGRESSION a:UJ (b = l) o. 300 ü. o < UJ 200~~

~~Ü I- UJ 2 100~~

~~100 200 300 400 500 ' " MEAN MEASURED DRAFT (lb)~~

FIGURE 94.—Relations between predicted and measured mean drafts for narrow vertical tillage tools operated in several soil conditions. (Payne, Jour. Agr. Engin. Res. {329 ).) not accurately predict the average draft of a narrow vertical tool. In its present form, the mechanics is not completely accurate. The wide range of tools and settings (ratio of depth to width ranging from 1:1 to 15 :1) and the range of soil conditions (cohesion ranging from % to 3 p.s.i.) was satisfactorily represented by the mechanics. Since the mechanics predicted a fairly constant excess of 25 percent in draft, hope exists that the mechanics can be improved. In addition to the possible errors discussed in this section, others mentioned in section 4.3.1 may also have been present. The dynamic soil parameters may not have been measured accurately, the behavior equations may not have been applied correctly, or the behavior equations themselves may not be accurate. Nevertheless, Payne has clearly demonstrated the principles for establishing a mechanics for narrow vertical tools. 4.3.3 Cutting of Soil Cutting of soil may be defined as the complete severing of the soil into distinctly separate bodies by a slicing action that does not result SOIL DYNAMICS IN TILLAGE AND TRACTION 149 in any other major failure such as shear. Figure 95 shows the effect on soil cutting of using cutters with two heights of soil lift and two depths of operation. In situation A in figure 95, the lift height of the cutter is sufficient to cause shear failure surfaces that reach the

~~//4i?^//^// ^my/^y/M'w^^/^ ^^/^/m//^^^^//^//^~~

~~(A) (B)~~

FIGURE 95.—Soil cutting as influenced by the height of lift of the cutter and depth of operation. surface of the soil. In situation B, however, the lift height of the cutter is not sufficient to displace the soil enough to cause major shear failure. In situation B, the soil mass separates with little evidence of any other action. Presumably, the soil was capable of absorbing the imparted strain without reaching shear failure. Thus, in situation C in figure 95, the soil is capable of absorbing the strain even though the same lift height as in situation A is used. To a certain degree, therefore, cutting as an action distinct from other failure of soil is determined hj the degree of confinement in the neighborhood of the cutter. Obviously, the size of the required neighborhood for a specific cutter will be influenced by the condition of the soil. A wet plastic soil may cut in situation A of figure 95, whereas a dry brittle soil may create shear failure even with a low lift height as shown in situation B. Cutting as affected by degree of confinement was further demonstrated by Kostritsyn ( 230 ). He studied vertical rather than horizontal cutters. The cutters could be described as thin knives, and he observed the soil movement caused by the cutter. The results of his observations are shown in figure 96. He noted that near the surface, soil would rupture or move upward (fig. 96,^); but at deeper depths, the movement was parallel to the direction of travel of the cutter. Figure 96, B shows the measured draft of the cutter versus the depth of the operation. Below a critical depth, a linear relation existed between draft and depth. The critical depth generally coincided closely with the observed depth where soil movement became horizontal. Kostritsyn reported that the critical depth was 20 to 25 centimeters for cutters approximately 3 centimeters thick. Thus, at deeper depths confinement of the soil causes pure cutting, whereas at shallower depths other types of soil failure also may occur. Kostritsyn described the soil movement near the surface as a 150 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~AP ^~~

~~V \~~

~~JC < Î \~~

~~(A) (B)~~

FIGURE 96.—A, Soil movement caused by a thin vertical cutter; B, relation of cutting force to depth of operation for a vertical cutter. (Kostritsyn {2S0 ).) crumbling action with the formation of crescent-shaped sliding bodies of soil. The description is similar to that used by Zelenin and Payne for vertical tools. Thus, although cutting can be clearly defined, in tillage tool operations it is not always clearly and independently involved. Obv^iously, a gradual transition from pure cutting to some complex action occurs as the depth of operation of a vertical cutter is decreased. A similar transition must occur when the depth of operation of a horizontal cutter is decreased or its lift height is increased at a constant depth of operation. Similarly, if soil conditions change from plastic to brittle, a transition from pure cutting to a complex action may occur. This lack of isolation of cutting has probably delayed its study, and no behavior equations have been developed to represent cutting. As a consequence, no dynamic properties of soil associated with cutting have been identified, so none were discussed in chapters 2 and 3. Detailed studies of pure cutting have been made in the U.S.S.E., and Kostritsyn ( 230 ) continued the studies to a point where he developed a mechanics of cutting. His work followed the efforts of several earlier researchers, and he relied heavily on their findings. An interesting difference exists between the development of the mechanics of cutting and the development of the mechanics of inclined and vertical tools. In the latter mechanics, the reaction of the soil to a tool was visualized to result from simple behaviors that had been identified and were quantitatively defined. Thus, such factors as shear failure and soil-metal friction were used as the basis on which to establish a mechanics. Kostritsyn, on the other hand, directly analyzed the action and in the process developed a mechanics. He did SOIL DYNAMICS IN TILLAGE AND TRACTION 151 not begin with behavior equations, but his mechanics implied the existence of a simple behavior equation. Kostritsyn's success in developing his mechanics hinged on evaluating the implied behavior equation. While he recognized the behavior, he proceeded to evaluate it by indirect means rather than by a direct study of the behavior itself. Thus, he did not develop a simple behavior equation that, in turn, identified behavior properties of the soil. Kostritsyn did, however, manage to assess cutting of soil in empirical terms—that is, numbers that are some composite of the overall action involved in cutting rather than a clearly defined independent dynamic parameter. On this basis, he was able to construct his mechanics so that he could represent the action of cutting. To illustrate the mechanics of cutting, Kostritsyn's analysis is presented in detail. Kostritsyn restricted his attention to situations where only pure cutting was involved. In developing his mechanics he did not consider that any major failures other than separation were present. He considered two basic shapes of cutters (fig. 97). The leading

~~(A) (B)~~

FIGURE 97.—Forces on and shape of two soU cutters. (Kostritsyn (230).) angled edge of the cutters he designated as the wedge of the cutter while the parallel edges he called the sides. He reasoned that the forces acting on a cutter could be separated into several components and these components must be in equilibrium so that

p = p, + P, + P,3^ (81) where P total force (draft) on the cutter, Pi component of resistance resulting from the normal force on the wedge of the cutter, Pn component of resistance resulting from the tangential force on the w^edge of the cutter, Ps component of resistance resulting from the tangential force on the side of the cutter. The forces are shown in figure 97, where N represents normal forces and T represents tangential forces. For a cutter shaped as 152 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE shown in figure 97, A, obviously P3 in equation 81 will be zero. If the simple behavior of soil-metal friction is recognized, the tangential forces can be expressed in terms of the normal forces and friction is identified as the source of the tangential forces. Figure 98 shows

~~fî=2{Nsin-f-) f| = 2(N^'cosf) P, =2(N,/*') (A) (B) (C)~~

~~FIGURE 98.—The components of force on a soil cutter. (Kostritsyn (230).) the resistance forces resolved into horizontal components so that equation 81 can be written~~

~~P = £ N sm-j- + ^ ^ f^' 00s ~ -^ £ Ni fi% (82)~~

where a = wedge angle of the cutter, ft' = coefficient of sliding friction, N = normal force on the wedge of cutter, Ni = normal force on the side of cutter. With equation 82, Kostritsyn could calculate the cutting force for a particular cutter if he could specify the magnitude of the normal forces. By reasoning that these normal forces resulted from the resistance of the soil to deformation, he defined measures of the resistance so that N = Ki F, (83) where Ki = specific resistance to deformation, Ft = area of the wedge of cutter, and Ni = K2F2 (84) where K2 = specific pressure of soil, F2 = area of the side of cutter. K2 differs from Ki in that Ki goes to zero when movement of the tool is stopped. K2, on the other hand, continues to press on the sides of the cutter even though the cutter is stopped ; it reflects an elastic type of restoration property in the soil. With equations 83 and 84, equation 82 can be rewritten to give

P = 2 Kt Ft sin -^ + 2 Kt Ft fJi' cos -^ -^ £ K2 F2 fJi\ (85) SOIL DYNAMICS IN TILLAGE AND TRACTION 153 Equation 85 provides a means for experimentally studying cutting. For a specific cutter, the values of «, Fi^ F2^ and /x' are known or can be determined and only Ki and K^ are unknown. By measuring P for a cutter shaped as shown in figure 97, A, Ki can be evaluated from equation 85 since F2 will be zero. If a similar cutter, but shaped as shown in figure 97, B is also used, the value determined for Ki and equation 85 are sufficient to evaluate ^2. Figure 99 shows the differ-

~~26.5 S (mm)~~

FIGURE 99.—The influence of thickness on the force on two shapes of cutters. (Kostritsyn, {2S0).) ence in force on cutters of several thicknesses measured by Kostritsyn. Having introduced the concepts of specific resistance and specific pressure {Ki and Z^, respectively) that originate because the cutter causes the soil to deform, Kostritsyn took steps to evaluate the amount of soil deformation caused by a given cutter. He accepted as a working hypothesis the results of earlier Russian researchers who demonstrated that the path of movement of a particle of soil follows the direction of the resultant force—that is, the path of motion and line of action of the resultant force will coincide. Figure 100 shows the paths of deformation for specific circumstances. If no friction occurs between the wedge of the cutter and the soil, a particle originally situated on the center axis of the direction of travel of the cutter will follow the path a'a shown in figure 100. During the forward movement of the cutter, the particle initially located at a' will be moved along line a'a to a. Where soil- metal friction is involved, the resultant force is inclined to the wedge by the angle of soil-metal friction 8. In this case, a particle is moved along the line a''a, as shown in figure 100. The maximum displacement of soil thus is not equal to the width of the cutter S. Because of the interaction between the wedge angle and the soil-metal friction angle, the actual path length is something greater than AS'. Having established the direction of soil movement, Kostritsyn could calculate the maximum deformation for a given situation. The 154 AGRICULTURE HANDBOOK 316, U.S. DEPT. OE AGRICULTURE

~~i ï~~

~~y4 4-^ y ^2 s / / b" b' b <~~

~~] '~~

~~FIGURE 100.—The direction of specific resistance, specific pressure, and the associated paths of deformation of soil particles. (Kostritsyn {2^0).)~~

maximum occurs when point a in figure 100 reaches the widest part of the wedge section of the cutter. The maximum deformation is shown in figure 100 in the triangle Wh'' ' where geometry indicates that the angle VW ' is (a/2 + 8) so that the length Vh is given by the equation

J-^max — (86) ^ cos {aß + 8) where S = width of cutter, 8 = angle of soil-metal friction, a = wedge angle of cutter, Lmaw = maximum deformation. The soil deformation along the wedge will vary from zero at the tip to the maximum shown in equation 86, so that average soil deformation Lo can be calculated by the relation 0 + Ln S Lo = (87) ^ COS (a/2 + 8) • Equation 87 applies to the deformation caused by the wedge portion of a cutter. Kostritsyn reasoned that no additional deformation occurs along the sides of the cutter, and the average deformation will be constant and numerically equal to that given for half of the maximum deformation occurring on one side of the cutter and expressed by equation 86. Kostritsyn argued that a relation must exist between soil deformation, specific pressure, and specific resistance. In reality, specific pressure and specific resistance are the normal stresses acting between the soil and the cutter. The value of specific resistance is the stress required to cause a given deformation. Kostritsyn recognized that such behavior is stress-strain be^havior (uniaxial compressive stress-longitudinal strain), but he also recognized that no suitable relation existed. Such a relation can be represented by a simple be- SOIL DYNAMICS IN TILLAGE AND TRACTION 155 hayior equation that would define dynamic parameters of the soil. With the direction of strain movement specified as discussed (the behavior output of the equation) the mechanics of cutting could be developed in a manner similar to that used by Soehne, for example. Recognizing the behavior equations involved and specifying the behavior outputs establishes a method by which to locate and orient the forces involved. Kostritsyn, however, by analyzing the cutting reaction, has worked backwards and shown the need for a specific simple behavior equation. The difference that was discussed earlier between the methods for establishing a mechanics thus should be apparent. Kostritsyn did not study a stress-strain relation directly, but rather indirectly through his mechanics. For a given cutter he could calculate Lo for the respective K values from equations 86 and 87. He could evaluate experimentally the magnitude of the two K values from equation 85 by using two cutters with different shapes. An example of the relation between Ki and K^, and their respective average deformations is shown in figure 101 for one soil in one condition.

~~23.2 Lo(mm)-K2~~

~~FIGURE 101.—Relation between specific resistance K^ and specific pressure K^ and the respective average soil deformations. (Kostritsyn ( 230).)~~

Several important conclusions by Kostritsyn are based on the general nature of the curves shown in figure 101. First, the two K values were not constant, so that they were not parameters assessing the soil. Since they represent stresses, constant values probably should not be expected. For the mechanics, however, a parameter must be found that is constant for a given soil condition. Second, the reversed trends for the two K values as the average deformation was increased indicate that some interaction between the soil and cutter must be occurring. If not, the trends should have been the 156 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE same—th^y should both either increase or decrease as the average deformation increases. Third, the low value of K2 suggests that some- how the normal stress on the sides of the cutter is reduced during the soil reaction. To illustrate, we might reason that the maximum stress caused by the wedge of the cutter remains acting on the sides of the wedge as long as the soil is forced to remain deformed. In such circumstances, Ki and K2 should be related by the cosine of the angle of the wedge. As the data in figure 101 indicate, the implied angle of the wedge ranges from approximately 150° to 180°. Since these angles are completely unrealistic, a logical conclusion is that the stress on the sides of the cutter represented by K2 is reduced by some type of relief. Based partly on the foregoing reasoning and partly on other observations, Kostritsyn proposed that the specific resistance and the specific pressure come from elastic and plastic deformations of the soil. He thus defined K, = Kei-^Kpi, (88) where Kei = stress from elastic deformation, Kpi = stress from plastic deformation. He further considered that K2 represented only the elastic deformation. These definitions imply that the soil deforms plastically and elastically as the wedge of the cutter advances. On the sides of the wedge, however, the soil has "adjusted itself" by plastic now so that only the elastic rebound of the soil causes the stress. As figure 100 shows, the lines of action of the hypothesized stresses are not parallel but are related by the geometry of the cutter. Since the directions of Ki and K2 do not coincide, K2 cannot be equated directly to the elastic component of stress in equation 88. From the geometry shown in figure 100, the magnitude of K2 in the Ki direction gives

Kei = K2 ^. (89) cos a/2 ^ ' With equations 88 and 89, the elastic and plastic components of stress can be calculated from the values of Ki and ^g. Figure 102 shows the respective values plotted against deformation, as determined by equation 87. Kostritsj^n determined the relation shown in figure 102 for several soils in various conditions. He concluded that the general shape of the curves was the same for all soils and then proceeded to obtain a mathematical expression for the curves. He noted that the relation between K^i and LQ was very close to that of an equilateral hyperbola so he used the equation

Kpi = ~-, (90) to express the relation. Close observation of the experimental data indicated that as Lo approached zero, the relation in equation 90 did not hold. This suggested that a minimum value for Lo existed and that it was equal to one or possibly several particle diameters. The minimum value Loo represents a small distance that reflects the unde- formable nature of individual soil particles. SOIL DYNAMICS IN TILLAGE AND TRACTION 157

~~X VALUE OF Kpi ACCORDING TO THE THEORETICAL FORMULA~~

~~10 II 12 ( mm)~~

~~FIGURE 102.—Calculated and experimental values of elastic and plastic stresses as related to deformation. (Kostritsyn {230 ).)~~

~~Associated with this minimum deformation is the constant Ko given by Ko = -^, (91)~~

where Loo = diameter of soil particles, Ko = maximum stress to cause deformation. Equation 90 was reasonably accurate as long as Lo was greater than Loo^ To overcome the restriction placed on equation 90, Kostritsyn used an equal area technique to evaluate the shape of curves and obtained the equation T> r û)T 1 5 r.. ^ 7 ^Loi (92)

~~where B = coefficient of plasticity. Kostritsyn then defined Kei = Ko-K,i, (93) and by using equation 90 and the equal area technique he obtained the equation~~

~~K,^ = -^ \KO (ßU - Uo) -In^i (94)~~

where A = coefficient of soil elasticity. 158 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Equations 92 and 94 take into account the restriction observed in equation 90. Coefficients Ä and B represent empirical constants that permit a more accurate representation of the relations between Kei, Kpi^ and Z^. Note that in equations 92 and 94, Ä and B represent constants for a given soil condition, as do Lô and Ko- Thus, in a sense they are composite soil parameters. They are not, however, parameters of a behavior equation but rather of a mechanics for cutting. Kostritsyn evaluated constants A and B for several conditions. For the soil represented in figure 102, he assumed Loo was approximately 0.5 millimeter. The coefficient B can be evaluated only from experimental data so that the value for Kpi at some arbitrary Lo is required Given the value for B, Kî can be determined for other values of Lo by using equation 92. The theoretical points shown in figure 102 were calculated from equation 92. Table 10 gives measured and calculated values for Kî and Kî for a different soil condition. Kostritsyn stated that the large percentage of error at 1-millimeter deformation was due to the inaccuracy of experimental apparatus for such small forces and deformations. As figure 102 and table 10 show, however, the experimental and calculated values agree remarkably well. Although Kostritsyn did not show data to compare the actual draft of the cutters, agreement of the soil stresses implies that the calculated and experimental drafts would have agreed just as well. Thus, the mechanics of cutting as developed by Kostritsyn is reasonably accurate and complete.

~~TABLE y),—Experimental and commuted values of the clastic and elastic stresses to deformation during cutting~~

Mean soil K,i Kel deformation Experi- Com- Experi- Com- (miUi- mental puted Differ- Differ- meters) ence mental puted values values values values ence Kg./cm^. Kg./cm^. Percent Kg./cm^. Kg./cm^. Percent 1 7.3 5.60 -2.5 0.212 0.330 +35 3 5.4 7.00 +3.5 .390 .405 +4 5 __ 4.1 4.05 +1.0 .440 .440 0 10 2.5 2.50 0 .465 .465 0 SOURCE : Kostritsyn ( . ).

In order to determine parameters A and B, the forces on an actual cutter must be measured experimentally. Therefore, the mechanics of cutting may seem to be a hoax. Such is not the case, however, if the means required to assess the magnitudes of A and B are recognized. As has already been implied, the parameters are defined by the mechanics rather than by a behavior equation. Kostritsyn argued that a stress-strain behavior equation must exist, but it is unknown. He proceeded to establish a relation indirectly through his mechanics where cutting is involved rather than a direct relation where the stress-strain behavior was isolated. His mechanics of cutting IS thus the mathematical model that represents the situation under observation. The mathematical model defines parameters A SOIL DYNAMICS IN TILLAGE AND TRACTION 159 and B; hence, they are parameters of the mechanics, not of stress- strain behavior. As was discussed in chapter 3, some method is always required to assess the magnitudes of parameters. Eecall that the usual procedure involves simulating the mathematical model and measuring the appropriate quantities in order to calculate the desired parameters. In this case, the mechanics is the model and hence an actual cutter is required. Once A and B have been specified, however, they can be used and applied to that soil condition just as independent parameters such as cohesion can be applied. The mechanics of cutting thus differs from the earlier mechanics only in the method required to assess the respective soil parameters. While the mechanics seems to be very accurate as presented by Kostritsyn, caution should be used in its application. Stress-strain behavior is probably inaccurately represented because of the indirect manner in which it was studied. No distribution of stress is ad- mitted to exist on the cutter when a distribution would seem logical. Whether the average stress and deformation accurately represent the implied behavior has not been determined. Kostritsyn apparently confined his experiments to wet dense soils. Experience tells us that such soils tend to be plastic and therefore probably only pure cutting was involved in the experiments. In many soil conditions plastic behavior may be less evident and the relation expressed in equation 90 may be drastically different. If a difference occurs, equations 92 and 94 may no longer accurately represent the situation. Even further, this possibility raises the question as to whether pure cutting will be present. As soil conditions change so that plastic behavior is less dominant, other types of failure may also be present and increase in importance. Kostrit- syn's mechanics applies only to pure cutting and would not represent such situations. Considerations of this kind limit the situations where the mechanics can be applied. A final consideration of the forces on a cutter suggest a possible component of resistance along the leading edge of the cutter. Such a force is present if large hard particles are visualized as being cut by an infinitely thin cutter, as shown in figure 103, A. In order for

~~(A) (B)~~

~~FIGURE 103.—The effect of boundary conditions on cutting.~~

the cutter to move from A to B along the projected path (fig. 103, A), several of the large particles would have to be sliced and separated. Contrast this action to the actions implied in Kostritsyn's mechanics for cutting, where particles presumably smaller than the cutter are merely displaced but not sliced. A possible fourth term 160 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE could thus be included in equation 81. This term might be extremely useful when evaluating the cutting resistance of materials in the soil, such as roots. Figure 103 also shows the effect a boundary condition might have on cutting. If a pile of coal were being shoveled from the top (a situation similar to fig. 103, A) rather than from a smooth floor (a situation similar to fig. 103, 5), the force to push the shovel into the pile would obviously be different. In the latter case, the boundary condition becomes orderly so that cutting is not required. Shoveling from the top requires deforming the aggregate of coal in an action similar to that represented by Kostritsyn's mechanics. The individual aggregates are displaced but not cut. Presumably an action could occur wherein the coal aggregates themselves would be severed so that an additional force would be required. Cutting per se is thus simply envisioned and easily defined, but its involvement with other actions compound and confuse the practical application of cutting. Getzlaff ( U2 ) has measured the effect of stones on the draft of plows and it appears that cutting or displacing rigid bodies can require considerable force. 4.3.4 Conclusions The examples of partial mechanics discussed in section 4.3 are the only examples presently available. They are restricted, occasionally based on questionable assumptions, and, as experimental evidence shows, not satisfactorily accurate. These shortcomings are acknowledged but do not detract from the fine efforts that have been made by Kostritsyn, Soehne, Kawamura, and Payne. Their analytical contributions have demonstrated the methods for developing a mechanics that integrates the soil and tool into a system that can be analyzed. Demonstrating that the actions involved m tillage can be represented by rigorous mathematical treatment is more significant than the practical usefulness of their mechanics. Even though the examples discussed here are not a complete solution, the scholarly approaches must be acknowledged as a break from traditional methods. Follow- ing the principles illustrated will lead to the development of a complete mechanics that will provide an understanding of soil-tillage tool reactions and that will ultimately have practical usefulness. 4.4 Soil Behavior in Simplified Systems Actual examples of soil-tillage tool mechanics have just been discussed. In each example, the mechanics was based on one or more behavior equations. The mechanics combined the active contribution of each behavior to the total action so that the whole reaction of the soil was represented. In chapters 2 and 3, a number of behavior equations that have been identified were discussed. In equation 18, two soil parameters 0 and (f) were identified, and ample evidence was cited to show their nature and importance. Not all behaviors have been so well studied. One principle for developing a mechanics is to identify the various forms of behavior that are present. Each identified form of behavior requires an accurate descriptive equation. One method for developing such equations is to separate the various forms of behavior that occur in the soil and study each behavior individually. Examination SOIL DYNAMICS IK TILLAGE AND TRACTION 161 of a total dynamic soil-tillage tool system indicates soil must always slide on the tool. In addition, sharp edges of a tool cut the soil ; and inclined surfaces lift, shear, or accelerate the soil. Each of these separate behaviors may be isolated from the others and studied m simplified systems. It may be recalled that the cutting component h was eliminated from equation 57 so that this type of behavior was neglected. In addition, no attempt was made to utilize friction except in an elementary form where the coefficient was considered to be a constant. Both of these behaviors are extremely important in tillage. So little is known about some behaviors that their intelligent inclusion in a mechanics is not possible. A discussion of examples of behavior study will show that attempts have been made to relate force inputs to soil reaction outputs. 4.4.1 Soil-Metal Sliding The importance of soil-metal sliding can be quickly grasped by anyone who realizes that all tillage tools have a sliding action. This action may not be the major action of the tool, but sliding occurs along some surface of the tool and consumes energy. Where control of soil movement is the major desired action, the kind of surface and its orientation govern the path of movement of the soil. Sliding behavior has not been exactly determined ; therefore, accurate behavior equations or simplified mechanics of the action have not been developed. Some of the principles were discussed in sections 3.2.1.5 and 3.2.1.6, but more accurate definitions of the individual relations and parameters are required. The basic equation that has been used in studies of sliding behavior is equation 29 F_ ^' z:. ^ = tan 8 (29) N The accuracy of this equation is determined by the assumptions involved. These include the concepts that the soil surface does not change during movement and that the normal force acting on the sliding surface is due to the weight or the mechanical forces applied to the surface. On the basis of past research, neither of these assumptions appears to be valid. Since actual behavior cannot be mathematically described at present, descriptive data to illustrate the complex behavior are presented. 4.4.7.7. Nieasuremenf of SUd'mgs Actions One method of determining whether the soil surface changes is to determine whether continued sliding over a given increment of soil causes a change in the coefficient of soil-metal sliding friction /x'. If a short slider is drawn over the surface of the soil, undisturbed soil is continuously renewed at the front of the slider. As the slider passes over a specific point on the surface, the surface may be changed by pressing and smearing so that the last increment of the slider passes over a soil surface quite different from that which the leading edge encountered. This fact may be experimentally determined by measuring with sliders of different lengths or by continuously rotating an annulus-shaped slider on the same spot. The basic question then becomes whether the change in the sliding resist- 162 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

ance is due to a change in ¡JL' or whether it is due to the extra loading of the frictional surface by adhesive forces. The basic behavior equation uses an input force, N, and an output force, F, Unless the equation is revised, the factor affecting the change m sliding resistance cannot be determined. In theory, friction should be independent of the area of contact; adhesive forces are not. A change in the adhesive attraction between the soil and the metal surface may therefore cause a change in the apparent normal load along the sliding surface and consequently result in a change in the sliding resistance. Adhesion may be increased through a change in the suction in the water of the moisture films or through an increase in the area of contact of the adhesive bonds. The action of these two factors must be separated and included in an evaluation of the sliding resistance between soil and metal. Sliding resistance may be visualized as a composite of friction and adhesive factors in the form R = u'N + ii'AF, (95) where B = sliding resistance, u' = coefficient of soil-metal sliding friction, N = normal load due to weight or mechanical forces, A = suction load due to water, F = area of the adhesive films. Attempts to evaluate equation 95 have been relatively few ; in most studies of friction the presence of the adhesive component fi'AF has not been recognized. In order to evaluate equation 95, the two terms must be separated and measured. Considering first the frictional term fju'N, the normal load may be determined from a knowledge of the weight of the material or by using pressure transducers to determine the normal pressure on the sliding surface. Tillage tools may be operated at high speeds, and the soil may be accelerated by the sliding surface of the tool. When the soil is being accelerated by the sliding surface, the additional force must be added to that of the weight of the soil. This force will be properly evaluated by the pressure transducer. Since the sliding resistance R can be measured accurately, fju' can be computed when the adhesive term is neglected. The actual value of N, however, IS still relative, since the pressure is not exerted through a continuous surface, but rather through a granular medium. Thus, for an assumed unit pressure based on the assumption of a continuous material, the actual area of contact may be very small and the granular pressure very high, or the area may be large and the pressure low. These details will not be detected by the pressure transducers. JNevertheless, for a given soil, there is a distinct relation between the average granular pressure measured by the transducer and that applied to the metal surface. This relation permits an empirical correlation between the normal load and the sliding resistance. The relation reflects the influence of such factors as the sharpness, hardness, and number of particles by lumping them in the coefficient ¡JL'. The adhesion term ¡JL'AF in equation 95 must also be isolated and each of the basic components measured. The term A may be considered to be the actual suction in the soil SOIL DYNAMICS IN TILLAGE AND TRACTION 163 moisture, but it may also include other forces such as magnetic at- tractions that might occur between the two materials. Some ano- malies that have been encountered in this assumption were discussed in chapters 2 and 3, and apparently additional work will be required to obtain a clear picture of the importance of the moisture suction term. A consideration of the attraction between the soil and the diaphragm of a pressure transducer shows that no deflection of the transducer occurs regardless of the magnitude of the attraction. Thus, the normal load detected by the pressure transducer does not and cannot measure this attraction. The suction in the moisture film may be measured by tensiometers, but they would have to be inserted into the sliding surface and have all of the characteristics of the sliding surface to provide reliable measurements. Formerly these instruments could be utilized only at low moisture suctions, but recent improvements have extended their range considerably ( 365 ). A major difficulty in dynamic sliding actions is the lag time inherent in tensiometers. The term F must represent the actual area over which the water films are effective. This area might be observed when glass models are used, but the area of the films within the soil is normally an unknown quantity. The extent to which approximations of the area, as might be deduced from measurements of bulk density, void ratio, and moisture content, can meet this need is not encouraging. When the entire normal load is applied by means of adhesion (sec. 2.9.3), the magnitude of the suction is known, the area of contact of the film is known, and the sliding force can be measured. Under such conditions the coefficient of friction ft' can be computed in the same manner as when the load is applied by a mechanical load. In practice, both mechanical and suction loads are operating on the soil so that the coefficient determined by equation 29 is an apparent coefficient and wdll be identified as />(.". It may be visualized as having the form R = ¡x'N.^-ixfN, = />t'W„ (96) where Ni — the load due to mechanical force, N2 — the load due to moisture suction, /x'' = the apparent coefficient of soil-metal friction. When N2 cannot be measured, the coefficient is determined on the basis of the applied load rather than the effective load, and the net effect of the second term of the equation, /xW^, is lumped into /x". The physical interpretation of this action has been to assume that an increase in the sliding force is due to an increase in the apparent coefficient of sliding friction /x'', and not due to an increase in the normal load (by factor N2) which results from adhesion. That the components of ft'' are not precisely known does not render equation 96 useless. The apparent coefficient />t" has been found to be a very useful soil parameter, but methods for determining /x' should be improved. Equation 96 implies that /x' as defined by equation 29 is not an independent parameter but is a composite parameter. As was discussed in section 3.2, independent parameters may become composite parameters as additional knowledge is obtained. Furthermore, 164 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE where no means is available to measure independent parameters, composite parameters must be used. Such is the case here, so that of necessity /A' and /i." are used interchangeably in the literature. The important point is to recognize that fi' is known to be a composite parameter. When used in a mechanics or applied to some situation, its composite nature should be acknowledged and appropriate caution used. Despite its vagueness, the concept of ¡J,' may be used to study the sliding action that smears the soil and changes the sliding resistance. One can determine the change in fi' that accompanies each successive increment of metal sliding over a fixed point m the soil. Soehne ( 397 ) used an annulus-shaped slider to study this type of soil reaction. Depending on the size of the ring and the number of revolutions, the length of the metal path that passed any point in the soil could be accurately controlled. Unlike a simple rectangular slider, which encountei-s new soil at the leading edge, all points under the sliding ring are subjected to approximately the same sliding distance. When the normal load on the slider is known and the sliding resistance is measured, the coefficient of .sliding resistance can be computed as a function of the actual sliding distance. Sliding rings of this type may be coated with materials such as rubber or polytetrafluoroethylene so that their respective values of fj.' can be determined (fig. 104). Soehne (fig. 105) found that fi' increased with an increase in the

~~FIGURE 104.—Simple sliders: Left, steel; right, polytetrafluoroethlyene; bottom, serrated steel. SOIL DYNAMICS IN TILLAGE AND TRACTION 165~~

~~8 12 16 20 24 28 16 20 24 28 SOIL MOISTURE {%)~~

~~(A) (B) (0~~

FIGURE 105.—Effect of the length of the sliding path on the coefficient of soil- metal friction for steel at different moisture contents: A, In sand; B, m loam; C, in clay soil. (Soehne, Grundlagen der Landtechnik (397 ).) length of the sliding path in sand A, loam B, and clay soil G, The increase in /x' resulting from an increase in the sliding distance was greatest at low moisture contents. Under the wettest conditions, the lesser influence of the length of the sliding path on the coefficient of soil-metal friction for steel was probably due to the low strength of the soil. When wet, complete puddling presumably occurred with the slightest movement and no further change was possible. Ad- hesion was probably not altered to any appreciable extent with additional movement. In contrast to a sliding surface of steel, rubber sliding over the soil presented a different relation. As shown in figure 106, little influence of the length of the sliding path appears in either sand A or loam soil B. In clay soil 0^ however, the coefficient increased

~~0.7 0.7 1 I.In '0.6 0.6 1.0 0.9-1 0.5- 0.5- O 8 ^04 0.4- 0.7 H 0.3 03 0.6 02 0.2-1 0.5 0.1- o = 30 cm O.l A = 60 cm 04 0 -T r- 0 2 3 4 6 10 14 18 22 26 8 12 16 20 24 28 SOIL MOISTURE (%) (C) (A) (B)~~

FIGURE 106.-Effect of the sUding path of the coefficient of ««iV'^^}>^^^,f^^^^^^^^^ at different moisture contents: A, In sand; B, m loam; 0, m clay soil. (Soehne, Grundlagen der Landtechnik {397 ).) 166 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE under dry conditions and decreased sliglitly under wet conditions. If the coefficient of soil-metal friction changes with the distance of sliding, it follows that the coefficient of friction expressed in equation 95 is an average coefficient when computed on the basis of a slider of finite length. The coefficient fi' represents a coefficient that lies midway between the initial coefficient /*'„ and the final coefficient /x'^, which are found respectively at the front and rear of the slider. The coefficient of sliding friction as determined by means of a slider is, therefore, Ä = M'XA^, (97) where x = the point along the slider of length L where the average fi' is found. According to Soehne, this average coefficient appeared to be located at approximately 04L along the sliding distance. This relation assumes that a uniform normal load exists on the slider. When the load along the sliding interface varies, the slider may be considered to be made up of n small segments each having an area Fi, an average unit pressure Pi, and a coefficient of friction fi'i, so that

E = X fi'iPiFi. (98) <=j Sliding resistance has not been calculated in this fashion and it cannot be determined from studies utilizing simple sliders. The distribution of normal pressure might be determined by means of pressure transducers. If pressure transducers were imbedded in a tool as shown in figure 107, the pressure at each of the small segments of interest could be determined. Mayauskas ( £95 ) used simple pressure transducers to determine the normal distribution along plowshares during actual field operations. The results are discussed in section 6.4.1.

FIGURE 107.—Pressure transducers for measuring stress distributions on sliding surfaces of tools. SOIL DYNAMICS IN TILLAGE AND TRACTION 167 A device is needed that will measure the tangential sliding resistance at the sliding surface. Taylor, at the National Tillage Machin- ery Laboratory ( 311 ), is among those who have attempted to develop such a transducer, but a successful model has not yet been produced. Many refinements are needed such as miniaturization, ability to separate movements in the various directions, and means for properly mounting the transducers in the sliding surface so that they measure the actual boundary conditions. The sensing element of the electrical strain gage can determine small stresses with insig- nificant strains. This permits an evaluation of the stress of the surface in order to get a detectable electrical signal for measurement. Care has to be taken that the exposed portion of the sensing element has the same characteristics as the surrounding material or the measurements may not reñect the desired forces. Figure 108 shows

~~-Tin^^^T^Tmñ, ^"~~

~~CELL CELL CELL CELL HIGH ROUGH LOW CORRECT~~

~~FIGURE 108.—Effect of placement of stress transducers (ceUs) on the soU flow pattern.~~

several situations that might be encountered if the transducers are improperly placed. Eecall that these devices would not measure the adhesive component of the normal force, but they would measure the tangential components of sliding resistance. Consequently, [x! as computed would be a composite value. An additional deviation from equation 29 is that \x! may change under loading so that it is a function of the normal force N. Ample evidence is available to show that the coefficient of sliding friction \i! is not independent of the normal load. In metals, McFarlane and Tabor ( 265 ) have shown that as the normal load increased the coefficient decreased until it reached a fairly low and constant value. In soil, decreases in the coefficient due to increases in the normal load have also been reported ( 9S^ ^65 ). Vetrov, using high normal loads and a simple slider on soil (fig. 109), showed that a constant value does not result from an increase in the normal load up to 7 kilograms per square centimeter (98 p.s.i.) ; hence, a value of ft' cannot be used with any degree of certainty unless the actual normal stress along the sliding surface is known. A word of caution is in order concerning the change in (xf with the sliding distance. Although Soehne ( 397 ) has proposed that this change be considered in the analysis of sliding forces on a plow, sufficient information is not available to determine whether this condition exists in practice. If the change in /x' is due solely to the smearing action of the soil, probably this condition would exist as indicated. On the other hand, if the change in ¡x' represents a transition stage when the metal changes from a clean surface to a dirty surface, only a conditioning of the surface to some new state may be represented. The end point—the stabilized value of /x'—would 168 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~0.6 -~~

~~""■""•- LOAM 0.4~~

~~0.2 "^ "''"•'=:ic:::^LAY LOAM ^"""-^^ CLAY~~

~~1 1 1 1~~

~~LOAD (Kg/cm^)~~

FIGURE 109.—The influence of the normal load on the coeflScient of sliding friction. {Vetrov (465).) depend on the soil materials that are deposited along the tillage tool surface. These coating materials might be waxes, moisture, fine clay particles, or other materials in soil. Surface coatings would account for the change in jx^ ; however, /¿' might be expected to remain fairly constant after equilibrium is established on the surface. After a plow travels far enough to coat the entire surface, a uniform value of /x' might be found for the entire surface. In a final analysis, both the soil surface and the metal surface may change. Physical reality must accompany raathematical representation of pressure distributions along sliding surfaces. The few pressure measurements that have been made along the sliding surfaces of tools indicate that wide variations may occur. If detailed studies are to be realistic, cognizance must be taken of interactions. Values of /x' must be determined for the entire range of pressures distributed over sliding surfaces. The extent to which this type of information may alter the concepts of theory or design is not known. As an example, it has been suggested ( 106 ) that a uniform pressure is required to produce a uniform acceleration of the soil. Actually, a uniform movement of soil across the face of the tool is desired ; and this may conceivably be obtained with different normal pressures along the surface of the tool. Let us imagine a distribution of pressure that might occur along a plow surface when shear failure occurs as visualized in the Nichols model (fig. 110). If all blocks of soil are to be accelerated with a uniform force, the resistance to movement of all blocks must be the same. This is not the case, since the shear force along the boundary between block A and the soil mass M is very large compared to that between any of the other blocks of soil. Theory then must SOIL DYNAMICS IN TILLAGE AND TRACTION 169

FIGURE 110.—Primary shear failure in front of a inoldboard plow. recoenize that the forces on the share of a plow are different from those on other parts. Equation 107 (sec. 4.4.1.3) incorporates this principle by keeping forces on the share separate from those ot the sliding surface. Little or no twisting of the furrow slice occurs at the forward part of the plow, but as the individual blocks progress up along the plow surface the forces on the plow vary considerably Indeed, the twisting action of a moldboard may pull the blocks apart so that gravitational forces actually cause overhanging segments to be placed in tension, as shown in figure 111. Obviously, the pressure on the surface of the tool goes to zero where the cracks appear. There seems to be little value in making additional theoretical

FIGURE 111.—Shear blocks spread by twisting of furrow slice. (Reed, Soil Sei. Soc. Amer. Troc. (S51 ).) 170 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE analysis of the movement of soil on tools until additional measurements provide a better basis on which to assign pressure distributions. As will be shown later (fig. 169), the pressure is not uniform so that this assumption no longer appears to be valid. 4.4.1.2 The Sliding Path In section 4.4.1.1, the direction of the sliding path was determined by the direction of movement of the metal surface. The actual sliding path over a surface is determined by the forces on the soil and the shape of the tool. The actual path of soil movement may be determined from the scratches that soil particles make on the surface of tools. If a tool is coated with a thin coat of varnish or some similar material, scratches can be easily detected (84), These scratches can represent the path of the soil only for the soil conditions and speed at the time the tool is operated. Kaburaki and Kisu ( W4 ) have identified and defined angles of sliding with reference to the direction of travel, as shown in figure 112. The angle S is measured between a horizontal line in the plane

~~ASCENDING ANGLE - ^ SLIDING ANGLE - S~~

~~PATH OF SLIDING PARTICLE~~

~~HORIZONTAL LINE~~

FIGURE 112.—Sliding and ascending angles of a soU sUding path. (Kaburaki and Kisu, Kanto-Tosan Agr. Expt. Sta. Jour. ( 204 ). ) of the sliding surface and the path of the sliding particle. A second angle, the ascending angle i//, was identified. It was measured from a horizontal line in the direction of travel and the path of the sliding particle. This angle might be utilized to compute the work done against gravity. A number of factors, such as the frictional and adhesive characteristics of interface systems, may be expected to affect the location of the sliding path. With the exception of the speed and the shape of SOIL DYNAMICS IN TILLAGE AND TRACTION 171 the tool, few of these have ever been studied. As shown in figure 113, both the particle size and the angle of inclination of a plane tool surface influence the angles of ascent and sliding. A knowledge of

~~90 ASCENDING X X 80 SLIDING~~

~~^ 50~~

~~UJ á 40 z < 30~~

~~0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 DIAMETER OF SOIL PARTICLE (mm)~~

~~FIGURE 113.—Effect of size of the soil particle and inclination of the tool on the sliding and ascending angles. (Kaburaki and Kisu, Kanto-Tosan Agr. Expt. Sta. Jour. {20Jf).)~~

the factors that govern the movement of soil particles will be helpful in the design of tools, since it becomes important to be able to direct the sliding of soil along predetermined paths. These paths may- direct the movement of the soil so that a minimum energy may be required for the movement or so that shearing strains will break up the soil. One of the more generally recognized directive actions is the inversion or movement of soil to some specific location at the boundary of a tool. 4.4.1.3 Mechanics for Draff force of Sliding Actions The foregoing material has been presented to describe soil behavior in sliding. The failure zone is predetermined by the interface, since any coupling between the slider and the soil results in shear or soil-soil sliding rather than soil-metal sliding. In the sliding actions that have been discussed, only fiat surfaces have been considered. The research that was reported was directed mainly toward determining the basic behavior equation and identifying the input and outputs of the equation. In addition, studies were directed toward identifying the basic parameters of the equation. The studies indicate that more basic relations must be considered before the data can 172 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE be used effectively in developing a mechanics. The alteration of the soil physical condition as a result of the sliding stresses creates a condition in which an interaction becomes operative. The importance of interactions of this type can be determined only by a more detailed examination. ^ Some progress has been made in developing simplified mechanics for sliding surfaces. In each instance, however, the coefficient of sliding friction was considered to be independent of the area of contact and adhesion. In addition, the ultimate goal of the mechanics was to evaluate the sliding resistance of the tool that was being considered. The basic behavior equation for sliding (equation 29) was accepted, and suitable boundary conditions were applied so that the inñuence of realistic force inputs could be evaluated. The first attempt to write a simple raechanics for soil sliding on a curved surface was by Doner and Nichols {106). They were concerned with the action of the curved surface of a moldboard plow on the forces on the sliding interface. (3rientation of the surface in some direction other than horizontal would alter the normal load because of gravity. The forces to be expected on a uniformly curved surface and on a variable curved surface w^ere determined. They considered that the force normal to the sliding interface of a co- hesionless soil and the curved surface was determined by three distinct components: the weight of the soil, the acceleration force, and a buckling force which was a component of the tangential force that causes the soil to slide. The first of these three forces—the weight of the soil on an area, A —IS a function of the inclination as shown in figure 114. The force due to the weight of the soil was calculated from the relation Wn = AhD^ cos a (99)

~~in which Ah = V = Acosa ,~~

and A = unit area of contact, V = volume of soil, a = inclination of surface from vertical, Dw = wet bulk density of soil, h = height of soil layer, Wn = weight component normal to surface. The second force on the surface was calculated from the equation mv^ = mv^k, (100)

where r = radius of curvature of the surface, m = mass of soil, V = velocity in the tangential direction, k = 1/r, I — inertia force normal to the surface. With a large radius of curvature and a slow speed of operation, the mertia force would be small compared to the weight, and it might be neglected. SOIL DYNAMICS IN TILLAGE AND TRACTION

~~FIGURE 114.—Effect of inclination on the normal force due to weight of soil. (Doner and Nichols, Agr. Engin. {106).)~~

The third force normal to the surface results from the resistance to motion along the surface and is called a buckling force (fig. 115). This force might increase or decrease the normal force on the surface, depending on the direction of the curvature. The buckling force may be calculated at any point on a curved path from the tangential and normal forces. At any distance S along the path, the forces may be resolved into a tangential force Ft, and a normal force Fn^ At a more distant point S +dS, the two forces would be correspond- ingly Ft + dFt and Fn + dFn^ Simultaneously with an increase m the distance S, there would be a change in direction of the normal force because of the curvature of the surface and the buckling eftect would be F,da = Ft^ds = Ftkds = Ftf{S)ds, (101)

The three forces were combined into a differential equation which has the form dFt = u'[P + f{S)Ft]ds, (102) where P = pressure on surface. Applied to a uniform curvature ä solution of equation 102 gives

~~Ft = j^{e-'^' 1). (103) 174 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE~~

FIGURE IW.—Left, The path of soil on a plow; upper right, the force on a small increment of soil; lower right, the buckling force on soil. (Doner and Nichols, Agr. Engin. {106).) or to a surface that had no curvature Ft = Pu'S, (104) When a variable curvature was introduced, f{S) had to be determined from the geometry of the surface. It was qualitatively determined that the curvature should be less at the share of a plow than at the wing in order to minimize the sliding force along the interface. The basic behavior relation described by equation 29 was thus utilized in a mechanical system in which the inputs and outputs were related to parameters of the physical system—the plow and the soil. The total force on a strip of the sliding surface was determined by equation 103, but no attempt was made to integrate the total sliding resistance of soil on an actual plow. Nothing in equation 103 indicates the optimum path that soil should follow on the surface of a plow. Eough approximations of shapes that provided paths giving minimum values of Ft were determined by trial and error for two hypothetical cases. Kawamura ( 207 ) analyzed the shape and action of a sod plow in which the normal forces were assumed to be constant on the sliding interface. In heavy sod soils, the plow inverts the soil in a continuous unbroken furrow. The movement is determined by the shape of the plow and the forces on the soil. Kawamura tried to determine the optimum path that the soil should follow to require SOIL DYNAMICS IN TILLAGE AND TRACTION 175 the minimum sliding force. The incremental frictional force on an elemental area results from the normal pressure and a component of the frictional force itself that is normal to the area due to the curvature so that equilibrium gives dR = -¡Ji' (PdS + Rde), (105) where B = sliding resistance, Jjf = coefficient of soil-metal friction, S = element of sliding path, 6 = angle of surface, P = normal pressure on surface. The path element dS may be expressed in terms of the radius of curvature r and the direction angle Ö, dS = rdO which upon substitution in equation 105 and integration gives the relationship B = e-'" (/ - fJL'Pre'"dO-hc), (106) If the sliding resistance E varies uniformly with increases in the length of the sliding path, there will be no pressure concentrations that would cause soil to stick to the plow\ The logarithmic spiral expresses a curve in which the radius of curvature varies with path length and when expressed in polar coordinates it has the form r = a6-^^ The minimum draft resistance of R of equation 106 would be attained when 6 = 0. Then a could be evaluated, and r =z roe-^\ Substituting this relation into equation 106 and integrating permits evaluating the constant of integration from conditions at the share where 6 = 0, S = 0^ and Ro is the resistance due to the share so that

~~R = e-^'' I Ro + -—^ (1 - e ('"-*=>'') (107)~~

where R = draft of plow, Ro = resistance due to share, P = normal pressure on surface, 0 = angle of sliding surface with horizontal, ^' = coefficient of soil-metal friction, k = constant. To — radius of path of travel. Evaluation of this equation with the aim of obtaining a minimum value of R indicates that k should be (9, which occurs when r = n and the path of the furrow slice is a circle. The sliding resistance R-Ro would be of varying importance depending on the conditions of the soil. Since part of the total resistance of the sod plow would be attributable to energy necessary for the deformation of the soil, Kawa- mura ( W8 ) introduced soil strength parameters into the analysis of the forces on a plow. Again, he considered the furrow slice to be continuous. Without further discussion of the methods he employed, the comprehensive equation he developed for the prediction of draft resistance for a plow having a circular path of soil movement had the form 176 AGRICULTURE HANDBOOK 316, U:S, DEPT. OF AGRICULTURE COS 20 ^^ M.sin^O Jeo I \fJi ht sinSI Q COS d ii^htL Wr cos Ö cos ^ H J (sin 6 + f/ cos 6) +

Tl^r sin 6 cos Ö cos 6?^, (108) and utilized parameters in terms which included : B = total plow draft, 0 = angle of soil twist in vertical direction, (j) ^ angle of twist in lateral direction, ¡uf = coefficient of soil-metal friction, L = radius of rotation of bottom of furrow slice, W = weight of furrow, g = acceleration of gravity, ht — distance from plow sole to neutral axis during bending, r = radius of curvature of plow, V = speed of plow, Mz = torsional couple, k = compressibility factor. Inherent in this equation is the consideration that the normal pressure on the sliding interface is a function of a weight term, an acceleration term, and a soil resistance term. Since experimental verifications of the relationship were not attempted, the accuracy of the mechanics is unknown. Like Doner and Nichols, however, Kawa- mura attempted to consider variations in the normal load on the sliding surface. A more detailed approach was made in this instance to specifically identify the origin of resistance in the soil. The couple Mg includes measures of the dynamic properties of soil. The bending moment is computed from shear stress-strain relations, the modulus of elasticity E^ the compressive stress CTC, and the tensile stress (Tt based on the size and degree of deformation of the furrow slice. Thus, we see that an attempt has been made to relate into a single mechanics the deformation and movement of the soil, the dynamic soil properties, and the forces required to cause soil movement. 4.4.7.4 Scouring One of the most important aspects of sliding action of soil is scouring of a tool while it is being operated. Since the coefficient of soil- metal friction of nonadhesive soil is normally less than that of soil- soil friction, less force is required to move a tool through soil if sliding occurs along the metal surface. Scouring is defined as the shedding or self-cleaning of the soil through a sliding action; but scouring also requires that the soil moves fast enough so that "too much congestion" does not occur. Thus, scouring is a relative term, rather than an exact term that designates the exact point where sliding begins. In normal operation where scouring is adequate, soil flows over a tool along a path that is determined by the shape of the tool. In adhesive soils, when sticking occurs, a layer of soil may build up along the surface of the tool so that soil flows over a layer SOIL DYNAMICS IN TILLAGE AND TRACTION 177 of soil attached to the surface of the tool. Figure 116 shows nonscouring and scouring surfaces.

~~FIGURE 116.—Surface of tools after plowing a sticky soil : A, Steel ; B, polytetrafluoroethylene.~~

In incipient cases of sliding, the soil moves across the tool so slowly that the soil on the tool acts as a rigid body which is driven through the soil mass. Soil does not flow smoothly across the plow \yhen this occui-s. Figure 117 shows the action of two plows shown in figure 116 in the same soil. The polytetrafluoroethylene-covered plow

FIGURE 117.- -Soil after plowing: Left, With good scouring; right, with poor scouring. 178 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE scoured and the steel plow essentially pushed the soil aside. The problem of handling a nonscouring so-called "push soil" is of general interest. As a rule, the adhesion between the tool and the soil is greater than that of the cohesion within the soil so that failure takes place withm the soil to cause nonscouring. Doner and Nichols ( 106 ) defined the scouring S at any point on a sliding surface as being approximately equal to the tangential force of the sliding added to the shear resistance of the soil F^ minus the trictional force at the same point ¡x'Fn. They concluded from their studies that plow curvature at the wing rather than at the share would reduce soil sticking. Payne and Fountaine ( 381 ) studied the mechanics of scouring along simple surfaces and concluded that the following factors affect the scouring of a tool in soil : ^1. The coefficient of soil-metal friction 2. The coefficient of soil-soil friction 3. The angle of approach of the tool 4. The soil cohesion 5. The soil adhesion They analyzed the equilibrium conditions at the point of scouring tor a simple system in which they considered only forces along the sliding surface. Figure 118 shows the forces as seen from above at

~~OPEN FURROW~~

~~COULTER CUT~~

~~FIGURE 118.—The geometry of a simple tool at incipient scouring. (Payne and Fountaine, Nati. Inst. Agr. Engin. {S31),)~~

incipient scouring of a vertical tool operating at an angle a to the direction of travel. The situation represents the case where the wedge of soil sticks to the tool; scouring does not occur. The forces at incipient scouring (thé wedge block of soil ABF just ready to move) will be R and Ä„ where the vertical plane BF has been separated by means of a tool such as a coulter. Since no tension forces perpendicular to the plane BF can exist, R and R^ must be equal and SOIL DYNAMICS IN TILLAGE AND TRACTION 179 colinear. They therefore constitute the maximum principal stress, and the minimum principal stress will be zero. Two possible soil failure planes can occur, and each will be oriented at (7r/4 +(/)/2) to a plane perpendicular to R. The worst situation for scouring is the formation of the plane AF, Presumably, once scouring begins, a failure plane originating from B in figure 118 will form and AF will not form so that the soil will be displaced and move along the tool surface AB, For the block of soil ABF to move, however, one of the failure planes in the soil must form. Since the criterion for failure is the same for both possible planes, the state of stress in the block of soil can be determined. The stress conditions may be represented in a Mohr diagram, as shown in figure 119.

~~FIGURE 119.—Mohr diagram of stresses on a simple tool at scouring when son-sou failure determines the stress. (Payne and Fountaine, Nati. Inst. Agr. Engin. {SSI).)~~

The strength envelope represented by the line LM can be drawn with a knowledge of ^, the angle of internal friction, and Í7, the cohesion of the soil. Since the minimum principal stress is zero, only one circle can be constructed that is tangent to the line LM and yet pass through Ö. Thus, the circle OG2R1 in figure 119 represents the state of stress in the block of soil ABF. Furthermore, the circle will represent the stress state at any incipient soil failure (failure by shear) whether or not scouring occurs. The one exception is if the angle a is large enough so that the failure plane AF is not permitted to form—if AB is parallel to AF, This exception is discussed m connection with figure 120. With the stress state determined by the soil shear failure, the stresses on the tool surface can be determined. By using adhesion and soil-metal friction as defined by equation 47, the condition for incipient scouring can be represented in figure 119 by the line HJ, Soil adhesion Ca is analogous to ¿7, and angle of soil-metal friction is represented by 8. For scouring to occur on the surface AB,, a stress state must be 180 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE present so that a tangential stress overcomes the resisting movement. Thus, stress states above the line HJ in figure 119 are the only stress states where scouring can occur. As already shown, the circle OGJRi represents the stress on any plane oriented with respect to the direction of R and Ri m figure 118. Thus, for a at zero in figure 118, the stress state on the tool surface will be Rt (zero tangential stress) in figure 119. As a is increased, the stresses on the surface AB change; the tangential stress increases so that at T in figure 119, the condi- fi^^fr^i incipient scouring are represented. From the principles of the Mohr circle, the angle TXR^ is 2a so that the minimum value of a tor which scouring will occur can be determined from figure 119 ^ IS further increased, the stresses on the tool will be those represented by a point on the circle, such as G. The stresses are above the tailure line HJ so that the soil will slide on the surface AB, The limiting relations between a, Ca, C, cf) and 8 thus are shown in figure 119 Obviously, if line HJ remains below LM, scouring can occur. It, however, S increases so that HJ is tangent between O and G2 and crosses LM between L and G2, scouring cannot occur for anv value of ce. -^ A special situation exists if 2a is greater than 90° + (^. The failure plane AF (fig. 118) will not be permitted to form; hence, R and /i*! will be determined not by soil shear failure but by the soil-metal tailure surface. Thus, the stress circle will be tangent to the soil- metal failure line, as shown in figure 120. For nonscouring in such

~~FIGURE 120 —Mohr diagram of stresses on a simple tool at scouring when A¿;'^Ain (^^i determines the stress. (Payne and Fountaine, Nati. Inst.~~

a Situation, the sticking soil (block ABF) must be a thin layer parallel to AB and the same normal stress must act on both the soil-soil surface and the soil-metal surface. To satisfy all conditions (circle through Ö tangent to HJ and also soil shear failure so that soil IS separated from the soil mass) the point of tangency must also be the point of intersection of the lines HJ and LM, as shown in figure SOIL DYNAMICS IN TILLAGE AND TRACTION 181 120. For any other circumstances, either the metal must fail in shear or a situation as shown in figure 119 will be in effect. Thus the relations between the factors governing scouring can be determined from the principles illustrated in figures 119 and 120. 4.4.2 Penetration Penetration is an action that may be described by a composite behavior since the soil usually fails by some combination of cutting, shearing, compacting, and ño wing (plastically) as a cutter or a probe is forced into the soil. As was discussed in section 3.2.2.1, failure during penetration is usually considered to occur in the immediate vicinity of the tip of the probe! Penetration is thus often termed cutting since cuttmg usually implies a localized soil failure in the neighborhood of the cutter (sec. 4.3.3). Although they were not discussed in section 4.3.3, Kostritsyn developed equations predicting the cutting force for cone-shaped cutters. Many so-called penetrometers are cone-shaped so that distinguishing between cutters and penetrometers is perhaps not realistic. In studying the behavior, researchers have used probes, cutters, penetration, and cutting rather loosely and interchangeably. Localized failure rather than the mode of failure is the common basis for discussing the behavior. Intui- tively, it appears that a penetrometer assesses soil strength, and the inherent simplicity of the measurement contributes to its practical usefulness. Thus, in spite of its composite nature, penetration behavior has been studied in some detail and has even been incorporated into a partial mechanics. The geometry of cutters or penetrometers is important because of its influence on the stress distribution in the soil near the tool. Consequently, the effect of geometry on penetration behavior has received considerable attention. The geometry may determine whether a tool acts as a knife-type tool that slides through the soil without soil sticking to its surface or whether it creates a compacted body of soil that sticks on its surface. As shown in figure 121, a compacted

~~(A) (B) (C) (D)~~

~~FIGURE 121.—The shape of compacted soU bodies on tools having different shapes. (Zelenin (515).)~~

mass of soil may gather on a blunt tip and move with the tool as an intricate part of the tool. At this time, primarily soil-soil friction is active since most sliding is between soil and soil. Even though a point is blunted or rounded, it may have little influence on the external appearance of the compacted soil body or core and on the 182 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE force required to move the tool in the soil. \s the shape of the tip approaches that of the shape of the soil body, the tendency for the soil to slide from the tool increases and ultimately the frictional resistance along the surface of the tool is reduced to where sliding begins. At this time, primarily soil-metal friction is active so that the force to move the tool may be less than when soil-soil friction is present. According to Zelenin (516), the compacted core appears when the angle of the tip exceeds 50°. Attempts have been made to determine whether the presence of the compacted body of soil influences the resistance to penetration. Data reported by the Waterways Experiment Station ( 472 ) indicate that the shape of the tip of the probe may have only a small influence on the resistance to penetration (ñg. 122).

~~Ü 200 abc fe 100 V) UJ oc CONE I5»C0NE a: 2in FLAT UJ ■ 45» CONE Ui O 10 ,<^>''n CONE 45» CONE de f ^lin HEMISPHERE 37* 30' GONE a.~~

~~UJ § 10 100 10 10 RESISTANCE TO PENETRATION (psi) PENETRATION (¡n) PENETRATION (In)~~

~~(A) (B) (C)~~

FIGURE 122.—Penetrometer resistance as influenced by shape: A, 30° static cone versus various-shaped static cones; B, 30° static cone versus various impact penetrometers at constant input energy; (7, 30° static cone versus various impact penetrometers with various input énergies. (Waterways Experiment Station (472).)

Figure 122, Ä compares a 30° right circular cone with flat and hemisphere-shaped tips. The measurements were made on slowly moving penetrometers and, with the exception of the cone, a compacted body should have been present. The data indicate little difference due to the presence of such a body. Figure 122, B shows the influence of cone angles of impact penetrometers. The impact measurement was made on a 1-inch cone, driven with one blow from a 1^-pound hammer dropped 4 inches. Figure 122, 0 shows the relation between a 30° static cone penetrometer and a 45° impact cone penetrometer where 5 inch-pound of energy (see curve a) and 8 inch-pound of energy (curve i) were used. For the 15° cone, 5 inch-pound (curve c)^ 7.5 inch-pound (curve d), 8 inch-pound (curve e), and 30 inch-pound (curve /) were used. At the higher energies and lower cone angles, deeper penetration resulted; but in all relations the slope was constant. SOIL DYNAMICS IN TILLAGE AND TRACTION 183 Since the slopes remained nearly constant over a considerable range of soil strength (from cone penetrometer readings of 10 p.s.i., which is soft, to more than 200 p.s.i., which is fairly hard for the clay soil used), it appears that either an impact or a static penetrometer could be used to measure penetration. Furthermore, interactions between the soil and the probe must remain constant for the various soil conditions, which tends to indicate that shape is not of great importance. Presumably, failure was restricted to the immediate neighborhood of the probe tip and the soil reaction was independent of the shape of the probe. Kostritsyn ( 230 ) extended his studies of cutting by investigating the effect of a fixed tool thickness on the cutting force while varying the angle of the cutter. With a triangular cutter, the forces on the cutter are as given in equation 85 except that F2 is zero because no sides are present. Thus, the forces on the triangular cutter are P = 2Kt Fi sin a/2 '\-2KiFt ¡i' cos a/2, (109) Avhere P — total force (draft) on cutter, Xt = specific resistance of the soil. Ft — area of wedge of cutter, a — wedge angle, ^' = coefficient of soil-metal friction. The area of the sliding surface can be calculated from the equation p ^ —^^—-^ (110) ^' ^sina/^' ^ ^ where 8 — thickness of cutter, e — length of cutter. As Kostritsyn demonstrated (sec. 4.3.3), Ki is a function of the deformation of the soil. The deformation is, in turn, a function of the wedge angle and the soil-metal friction angle, as shown in equation 87. For a constant tool thickness he thus proposed that

~~^1 = cos {a/2T^^X^' -^ oy (111) where Z) = a constant, 8 = angle of soil-metal friction. Equations 110 and 111 can be substituted in equation 85 and, recalling that fji = tan 8, the equation becomes~~

/.= " - [i+cot -^tansl, (112) cos(a/^ + 8) L 2 y where G — DSe, a constant. Equation 112 does not represent a mechanics since no rneans is available to determine the magnitude of C; hence, the magnitude of P cannot be determined. Kostritsyn reasoned, however, that an optimum wedge angle should exist and equation 112 implies that such an optimum will occur independent of the magnitude of 0 since it 184 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE is a constant for a given soil and thickness of cutter. He thus assumed C - 1 and calculated P versus a relationships at various soil- f riction angles. Figure 123 shows the relation for three angles of soil-friction;

~~UJ o Q: o~~

~~e> z~~

~~3 Ü~~

~~10 20 30 40 50 60 70 80 90 100 an~~

~~FIGURE 123.—Computed cutting force as a function of wedge angle for a constant thickness of cutter at 3 angles of soil friction. (Kostritsyn {2^0),)~~

45°50' and 29° are angles of soil-soil friction i//, and 40°30' is the angle of soil-metal friction 8. The data indicate that a minimum force occurs at a wedge angle at approximately 45° regardless of the type of the angle (i// or 8). Thus, even if soil sticks to the cutter so that soil-soil friction becomes active, nearly the same optimum wedge angle results. The 45° friction angle shown in figure 123 is a typical soil-soil friction angle, according to Kostritsyn. He reported experimental data that tended to confirm his calculated results. A minimum cutting force would thus appear to result regardless of the magnitude of the cutting force, and this minimum occurs at a wedge angle of approximately 45°. Perhaps the most thorough study of the influence of the geometry of penetrometers on resistance to penetration was made with dimensional analysis techniques by Kondner and associates {85-87, 223-227), While Kondner envisioned his tools as model footings, their cross-sectional area was less than 3 square inches. Dimensional analysis gives the functional relationship between tool and soil variables as SOIL DYNAMICS IN TILLAGE AND TRACTION 185

where QG = penetration, t — time, F — total force, G = perimeter of tool, A = cross-sectional solid area, 0 — tip angle of tool, T = maximum unconfined compressive strength of soil, 7) = viscocity of soil. The dimensionless terms were interpreted by Kondner to reflect certain physical characteristics of the system. The dimensionless terms in equation 113 reflect, respectively, penetration (the dependent W G^ . variable) ^, strength ratio of soil -j-^ shape effect of tool ^, tip characteristics Ö, and rate of penetration as influenced by viscous creep of the soil —. By allowing time for equilibrium during a static test and by maintaining a fixed tip angle, the last two terms in equation 113 are constant so that the relation simplifies to

Kondner proceeded to investigate the relations implied by equation 114. He first used circular footings (Ö = 180°) of varying cross o sections. For circular footings, the term j^ is a constant value equal to 47r, so that equation 114 reduces to the first two terms. Figure 124 shows data for one soil condition. The scatter m the dimensionless plot may have been due to experimental error or possibly to an oversimplification in that the creep term was assumed to remain constant. Even with the error, however, the dimensionless terms collapse the data very effectively. Kondner also conducted laboratory experiments in which he varied r, and the dimensionless relations again agreed well. He also reduced field data reported by a highway research board, and the dimensionless relations agreed well. In the latter, circular plates ranging from 1 to 7 feet m diameter were used. The relations between the terms shown m the dimensionless plots of figure 124 thus appear to be reasonably accurate. To study the shape factor ^, Kondner used models having a solid cross-sectional area of 2 square inches but varying perimeters. A circular footing gives the lowest possible ratio for any geometrical section. By using squares, rectangles, and crosses he was able to yaj.y _Ç from 16 to 136. A dimensionless plot of the relation indicated in equation 114 resulted in a good collapse of the data. When plotted as shown in figure 124, the data grouped about lines of con- 186 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~2 4 6 8 0.5 1.0 1.5 2.0 2.5 F (Kg) _F AT~~

~~FIGURE 124.—Force-sinkage relationships for circular footings: Left, Plotted in conventional terms; right, plotted in dimensionless terms. (Kondner, Waterways Experiment Station ( 22Jf ). )~~

~~0.100~~

~~0.075 ^ = CONSTANT = G~~

~~x|^ 0.050-~~

~~0.025~~

FIGURE 125.—Dimensionless plot of x/c versus c^/A for constant F/AT. (Kondner, Waterways Experiment Station {22Jf ).) SOIL DYNAMICS IN TILLAGE AND TRACTION 187 g^g^^l- ^^ Figure 125 shows the data plotted against the shape factor -Ç. The data indicate that greater penetration occured for a load as the ratio of perimeter/area approached a minimum. The consistent collapse of data about lines of constant terms (terms m equation 113) confirmed the implied functional relation. Kondner attempted to investigate the viscous creep term ^, which is important in a dynamic situation such as the vibratory cutting of soil. He made some progress but concluded that the relation was complex because the viscosity appears to be a function of the stress level. For static situations, however, the term could be considered essentially constant if the test were conducted slowly with time allowed tor equilibrium. Kondner thus concluded that equation 113 could be reasonably simplified to (115) when applied to slowly moving or static penetration. Kondner attempted to determine the functional relation represented by equation 115. Figure 126 shows a series of experimental

~~-y^~~

~~£ = 4tr 273 42.1 97,6 371~~

~~FIGURE 126.-Experimental footings having constant cross-sectional areas but varying perimeters. (Kondner, Waterways Experiment Station ( 22^ ).)~~

footings used in these studies. He also used a series of circular footings of constant diameter having tip angles of 15 ,30 , 45 , bU , yu , 120° 140°, and 180° and hemispherical shape. The results ot the varying shape factor on x/c are shown in figure 127- The exponent- ial nature of the curve shown at the left m figure 127 suggested the logarithmic relation indicated at the right. The^ intercepts and slopes of the logarithmic relation are functions of the strength term F ¡AT, SO that the slopes and intercepts could be related to the strength term. The relations were simple enough so that an equation could be developed as follows: 188 AGRICULTURE HANDBOOK 316. U.S. DEPT. OF AGRICULTURE

~~FIGURE 127.—Dimensionless plot of x/c versus c^/A for various geometrical shapes: Le/i, Arithmetic relation; rigU, Log-log relation. (Kondner, Water- ways Experiment Station {22Jt).)~~

G where h = constant, d = constant, S = constant. The magnitudes oih, d, and S are determined by the specific relations of the intercepts and slopes to the strength term. Figure 128 shows the results of the varying tip angle upon — when expressed G

~~5r;c, C2 C3 C4 c, C«C'6 ^7~~

~~^= CONSTANT =C~~

~~Í2 I~~

FIGURE 128.—Dimensionless relation between tip angle and Denetratinn fnr circular penetrators. (Kondner, Waterways ExpSnt StaCn [Ä ). SOIL DYNAMICS IN TILLAGE AND TRACTION 189 in a logarithmic relation. The slopes and intercepts of the constant strength term could be related to the term to give an equation

-^ = /(lOÖ)-^/^ (IIT) G where / = intercept, Q — angle in radians, m = slope. The relation between / and m and the strength term was not as simple as for the data shown in figure 127. Equation 117 could not be made as descriptive as equation 116, since the intercept and slope are not constants. Equations 116 and 117 are not presently useful since they are restricted to the soil conditions Kondner mvestigated. Furthermore, equation 117 is restricted in application to circular shapes where c^/A is a minimum and equation 116 applies when Ö has a constant value. If equations 116 and 117 could be combined into one expression, i\\<^ latter restriction would be eliminated. The most important contribution by Kondner is the accuracy ot the combination of variables indicated in equation 113. They permitted him to consistently collapse data to an acceptable degree. Furthermore, he demonstrated techniques for actually determining the behavior equation describing the composite behavior, penetration. The geometry of cutters must be studied further to reconcile the differences that appear to exist. As an example, occurrence of a minimum cutting force as determined by Kostritsyn is not reflected in the data of either the Waterways Experiment Station or Kondner. The occurrence of minima such as those due to the circular shape and the cutting angle must be sought and verified because of their importance in the design of practical tillage tools. Zelenin {51S) has developed empirical relations between the draft force of a cutting tool and physical conditions of the soil as measured by a penetrometer. The relation was developed to the point Avhere it constituted a partial mechanics. Zelenin conducted a large number of experiments in which he used horizontal cutters of the type shown in figure 77 and measured the draft and depth ot cutting. The size of the cutting tool and depth of operation were such that pure cutting as defined by Kostritsyn (sec. 4.3.2) was not the only quantity being measured. Thus, types of soil taiLure m addition to pure cutting were involved. Zelenin observed that the draft and depth were parabolically related according to the relation p = M^ (118) where P - cutting force (draft) of a horizontal blade, h — coefficient of soil resistance, h — depth of operation, fi = coefficient. Based on a wide range of soil and moisture conditions, the value for n was found to be approximately a constant whose value was 1.35. Zelenin further observed that the coefficient Jc was directly proportional to 0, the number of blows of an impact penetrometer (sec. 190 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE 3.2.2.1), when a specific blade was used. He thus proposed that equation 118 could be written as P ^ ACh'-'^, (119) where G = number of blows to penetrate a depth of 10 centimeters, A = tool geometry factor. With numerical values of O available for assessing the soil under consideration, the possibility exists that the draft force could be calculated if A could be evaluated for a particular cutting blade. Zelenin proceeded by first investigating the effect of the length of the cutting blade. He used a series of cutting blades where all factors were constant except their length Z, and from equation 119 he was able to show that A=l-h2.6L. (120) The angle of inclination of the blade a also influences the cutting torce. Zelenm showed that the cutting force varied with a accord- mg to the following relation P = Pi (1-h 0.0075a), (121) where Pi = cutting force at a = 20°, a = angle of inclination Equation 121 holds for values of a greater than 20°. For values of a less than 20°, Zelenin stated that equation 121 would have the constant value of P,. He also reasoned that if cutting was done on side walls (those parts of the tool that reach from above the soil sur- lace to support the horizontal blade), the angle of sharpening and the thickness of the sides would also affect the total cutting force Again from measured data he was able to show that with all other factors constant the cutting force varied as P = Pi {1 +QMS), (122) where Pi = cutting force at AÎ = 1 cm., S = thickness in cm. The effect of angle of sharpening was small so that it could be given by a coefficient ß^ whose value depended on the angle of sharpening Zelenin observed that the value of ß^ for angles of sharpening of 45°, 60°, 90°, and 180° was, respectively, 1.0, 1.01, 1.03, and 1.05. Equations 120, 121, and 122 can be combined with their respective restrictions to generalize equation 119 so that it becomes P = Oh'-''{l + 2.6L) {1 +0.0075a) {l-\-0.03S) ßo. (123) A comparison of measured and calculated (by equation 123) values tor various cutting tools as reported by Zelenin is given in table 11 The data agree reasonably well and show that a composite soil parameter can provide practical usefulness. Eeaves, at the National Tillage Machinery Laboratory ( 311 ) studied the accuracy of the basic coefficients in equation 123. He found that the exponent 1.35 may vary considerably with depth and soil type, so that care must be exercised when utilizing equation 123. SOIL DYNAMICS IN TILLAGE AND TRACTION 191 While empirical, new techniques and refinement may improve the accuracy of equation 123 so that its usefulness will be greatly extended. Certainly the methods followed by Zelenm are to be recog-

~~TABLE 11,—Experimental and calculated results of the cutting force on a simple tool~~

Measured Computed Difference draft draft (kilograms) Kilograms Percent 305 290 -4.9 260 258 - .8 620 580 -6.5 1400 1,470 + 5.0 1 200 1,130 -6.0 700 747 + 6.7 SOURCE: Zelenin {515). nized as valid and practical even though the approach is based on composite behavior. 4.5 Geometry of Soil-Tool Systems The mechanics of soil reactions to tillage tools cannot be developed fully until the inputs and outputs of the equations of dynamic behavior are identified. The principles by which this may be done were discussed in section 4.2, and specific examples showing how these principles have been applied were discussed m section 4.3. It is evident, however, that soil reactions in general have not been characterized to the point where they may be adequately described. In view of this, a number of studies and observations have been undertaken for the purpose of identifying the specific forms of behavior that are of interest (sec. 4.4). The lack of definition can be resolved only by additional information concerning the actions. Eventually, sufficient detailed information concerning each behavior should be available so that either additional or more accurate behavior equations can be established for incorporation into the mechanics. The exploration of the action of soil-tillage tool systems has shown that variation of tool geometry factors may be associated with the behavior output. In the qualitative phase of the development ot a mechanics (fig. 76), the inputs and outputs may be associated with overall causes and effects of complex tillage tool actions on the soil. Changes in the inputs may be associated with the methods by which forces are applied to the soil rather than associated with the torces themselves. . .. .î . i ^ i^ ;^ Variations in the geometry of soil-tillage tool systems result m different draft requirements for tillage and in different soil reactions. The influence of changing boundary conditions is so great that it has provided a means by which to study tillage actions of the system. Usually the tool is introduced into the soil and all failure occurs m the soil rather than in the tool. Therefore, the mode of soil action can be controlled by varying the geometry of the soil-tool system so that forces, their distribution, and the soil reactions vary. The exact 192 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE nature of forces altered by such changes is not known, even though It IS recognized that they may be varied. Eventually the soil reaction should be predictable from the strength of the soil as characterized by dynamic parameters and from the boundary conditions imposed by the tool as characterized by its forces and distributions. This will not be possible, however, until the action is identified and quantitatively described. At that time the tool can be eliminated from the soil system and represented by a series of forces. 4.5. T Alterafion of Tool Geometry by the Formation and Ad- herence of Soil Bodies Buildup of soil along the sliding surfaces of tillage tools may alter their shape. Soil adhering to the tool can form a body of soil that acts as a part of the tool. The presence of this soil body on the forces and soil reactions is of great importance. Any description of the shape of a tool that does not include the geometry and action ?i aô ^^^^ ^^^^ ^^^^ ^^^ represent the true system. Workers in the U.b.S.K. have described a number of these soil bodies {515), It was this type of soil body that Payne identified as a wedge in figure 89. Since he observed the wedge to move, he needed two behavior equations—one using î' and the other using ¡x. Had the wedge not moved, he would have needed only the behavior equation using /x. The shape and size of the soil mass that sticks to the tool is determined by the direction and movement of the tool and the eroding action produced along the sides of the soil body. The absence of scouring (sec. 4.4.1.4) creates the situation in which soil bodies are formed. Probably the soil in the soil body is replaced either piece- meal or en masse from time to time, but its presence as an integral part of the tool is definitely established. If the coefficient of soil-soil friction /x IS greater than the coefficient of soil-metal friction /¿' along the tool, the draft of the tool will increase. In addition, however, the draft of the tool may increase because the adhering soil increases the size of tool. Soil bodies also change the geometry of tools to the extent that the flow of soils may be directed into undesirable directions. Figure 129 shows the shape of soil bodies that were formed on simple chisels operating at a constant depth with different rake angles. The rake angle is defined as the angle between the face of ÜiQ> tool and the horizontal line of travel. These compact wedges were formed on the surface of the tools and were so tightly bound to the tool that they could be removed intact with the tool. Similar bodies have been observed on subsoilers (see fig. 131) and other tools. A first step in the study of this geometrical factor has been to identify and describe the soil bodies found on tillage tools. Dinglinger {103 ), Rathje ( 3J^2 ), Zelenin ( 515 ), Payne {329), Tanner {^19), Kaburaki and Kisu {205), and Nichols, Reed, and Reeves {32^) have observed and reported different types of soil bodies. Beyond these initial studies, which have established the fact that such soil bodies are present, little quantitative research has been conducted. No doubt the main reason is that soil bodies are formed beneath the surface of the soil under dynamic—sometimes transient—conditions so that they are difficult to observe and evaluate. Since the forces operating on a soil body tend either to form or to remove the body, its shape is probably extremely variable. Figure SOIL DYNAMICS IN TILLAGE AND TRACTION 193 130 shows compacted soil bodies that were formed on the surface of a tool at two speeds. The photographs are frames from a movie film of the tool operating in a clay soil. One side of the soil bin was

FIGURE 129.—The shape of soil bodies formed on a straight chisel operating in sandy loam at vario>is rake angles: A, 20°; B, 45°; C, 76°; O, 90°; E, 104° ; F, 135°. 194 AGRICULTURE HANDBOOK 316. U.S. DEPT. OF AGRICULTURE

Pioi-RE 130.—Soil body formed at two tool .speeds: Left. O.Ol.'i in.p.Ii. ; right, O.r» m.p.h. glass, and formation of tlie soil body could be observed by operating the tool adjacent to the glass. Thus, at least one visual technique is available by which to study the formation and efl'ect of soil bodies. While it is not evident from figure 1.'50, in the movies tlie body ap- jieared to be sliglitly smaller and more compact at the higher speed. Payne {329) used soil tracers to follow flie path of soil into the wedge. Simple geometrical tool parameters siich as length, width, depth of operation, and rake angle cannot be' used in a soil-tillage tool mechanics without caution. These values may be of little physical significance when soil bodies are formed. Indeed, formation of soil bodies may have limited the succe.ss of the principles of dimensional analysis and similitude in a study of the dynamic action of tillage tools. An actual soil body formed on a subsoiler is shown in figure 131. The presence of a soil body of tliis type would prevent one from determining the coefficient of soil-metal friction when utilizing vertical and horizontal forces as measured on a simple tool ( 332, 465). On the other hand, the ])rinciples of scotiring (sec. 4.4.1.4) might indicate that polj-fetrafluoroethylene coatings, small angles of approach, and nonadhesive soils could eliminate the formation of soil bodies and permit a more accurate analysis of tool reactions. Kaburaki and Kisu ( 205 ) appear to be the only workers who have studied the strength of soil bodies. They have reported that large flat sheets of soil which covered moldboard plows had a greater resistance to penetration near the share than higher on the moldboard. The compaction ¡¡attern they observed may be logically explained on the basis that pressures are higher on the share of the plow than on the moldboard. 4.5.2 Alteration of Tool Geometry Because of Wear The forces on tools remain constant only as long as the geometric conditions of the tools are maintained. It may not be possible to maintain constant conditions in a tillage tool oi)erating under field conditions. Rock, roots, or layering in nonhomogeneous soil may cause point loading. In addition, wear of a tool may change its geometry. The amount of metal lost through abrasion may not be as important as the manner in which it is lost. If abrasion changes SOIL DYNAMICS IN TIIXAGE AND TRACTION 195

FIGURE 131.—A soil body formed on a subsoiler during tillage of a dry clay soil. (Nichols and Reaves, Agr. Engin. ( 322 ).) the geometry of the tool, the forces on the tool may not remain fixed. In most cases the wear of a tool beyond the point where a refined degree of polish promotes scouring results in an undesirable situation. An analytical study of the alteration in forces due to the change of geometry by wear was made by Gavrilov and Koruschkin ( HO). Based on the observation that wear occurs along the underside of the tool, the angle of change in sliarpness of the tool a was visualized as shown in figure 132. As wear increases on the underside of the edge, the clearance angle y decreases to the point where it could become negative and in fact become an angle of approach. When it becomes an angle of approach, there is no longer clearance under the tip and 196 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~X-^ FURROW BOTTOM~~

~~(A)~~

~~FIGURE 132.—Edges of tillage tool: A, Sharp; B, worn. (Gavrilov and Ko- ruschkin, Selkhozmashina (I40).)~~

a larger area of the tool is in contact with the soil. Under severe wear conditions, the angle can increase to the relative magnitude shown m figure 132, B so that a normal force B develops on the front oí the worn surface Ä0. Soil-metal friction changes the direction ot the resultant force to Ä, = A/cos S. With a forward movement ot the tool, a horizontal resistance P^ develops in front of the tool. Ihis resistance is related to both Ri and R in the form Pi = Risin (8 + 7), (124)

orPi=R sin (^\ (125) \COSÔ/ Equation 125 can also be expressed in the form Pi - R (tan 8 cos 7 +sin y). (126) Since tan 8 represents the coefficient of soil-metal friction, it should be possible to determine relations between P^ and y for a fixed value of 8. By equating the first derivative of equation 126 to zero, a relation can be obtained where

P' — R (cos y - tan 8 sin 7) = 0. (127) When P' becomes a maximum (fig. 133), it is possible to establish a relation between 8 and y having the form cosy tan 8 sin y tan y* (128) Thus, when Pi becomes a maximum, there is a reciprocal relation between the angle of sliding friction 8 and the approach angle y. In practical situations, this relation might determine the final shape of the wear pattern at equilibrium. The frontal pressure that is applied to the underside of the tool for a unit of width would cause a moment M^ about the point O which would tend to lift the tool out of the ground (fig. 132). SOIL DYNAMICS IN TILLAGE AND TRACTION 197 150

~~r n~~

~~FIGURE 133.—Relation of the clearance angle 7 and the force P^ when 5 is 25°. (Gavrilov and Koruschkin, Selkhozmashina {I4O).)~~

~~(129)~~

where Ri = ^, cos Ô L = cos (8 + 7) * On a small increment of the surface along AC, R xdx (130) dM = coso COS (8 + 7) ' and when x = B cos y, R B^ cos y (131) M = 2 cos^ 8 - sin ^ 8 tan y The moment M results in an upward component of force so that vertical stability of the tool may be reduced because of the worn edffe Wear occurs over the entire surface of the tool, but this type of wear normally changes geometry less than wear at a tip or cutting edfi-e Areas over which surface wear is most severe may be estimated by a technique used by Pfost (334), Varnish covering the surface of the tool will be worn away by soil abrasion. As shown in figure 134, the progress of wear, as determined by the loss o±

~~40 Ft. 80 Ft. 200 Ft.~~

FIGURE 134.—The progressive pattern of surface wear as affected by the distance plowed. (Pfost, Auburn Univ. (334).) 198 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE varnish with the distance of travel, indicates the leading edge to be the zone of high pressure and wear. The relative importance of other areas becomes evident as the distance the plow travels is increased. Ihis technique may be used to qualitatively determine the relative importance of wear on different areas of a tool. Unfortu- nately, until the behavior equations of wear are developed, a mechanics of wear cannot be developed. Areas of wear can also be determined by measuring changes from the original profile of the tool, but the measurements are laborious. A number ot workers have measured this in terms of weight loss. Koopman ( ß28 ) built a small apparatus with which thi profile could be measured at any time without having to resort to laborious measurements. Wear is a most important practical consideration in maintaining proper microtool geometry. Data are not available to indicate the extent to which geometrical changes caused by wear affect soil reactions or forces on tools. Until data of this type are available be determSed™^^'"*''''''^ °^ maintaining geometry of tools cannot 4.5.3 Soil-Tool Geometry While tillage tools may have fixed shapes, their geometrical relations with the soil they contact may be altered with respect to the surface of the soil, and to their direction of travel and mode of operation. As a consequence, the forces applied to the soil by the tool may vary considerably as does the soil reaction. In many cases, altering the soil-tool geometry provides a means of studying complex tillage actions. By determining the influence of various geometrical arrangements on the draft force or the nature of soil breakup, individual types of behavior can possibly be isolated within a gross tillage reaction. Many studies have been directed toward establishing relations between orientation of the tool and the draft force. Zelenin ( 5J5 ) has measured the forces on narrow cutting tools operating with nonsymmetrical soil boundary conditions. Eesults show that the perimeter of cut per se is not sufficiently definitive to describe the soil-tool system (table 12). The degree of confinement ot the soil as induced and controlled by the geometry of the cut materially affects the draft force of the tool. A perimeter 39 centimeters long that IS cut at a depth of 15 centimeters with no sidewall cuts requires a force 40 percent larger than a perimeter 38 centimeters Jong that is cut at a depth of 7.5 centimeters and includes two sidewall cuts. Thus, interactions between the soil and the tool that are manitestations of the geometry prevent the use of any simple relation between the length of the soil-tool perimeter and the draft force, btudies ot cuts of various depths and widths, such as the one reported here, give an insight into the contributions of depth and width to the cutting force. The discussion of soil cutting in section 4.3.3 and the nature of soil movement shown in figure 96, A demonstrate that soil near the sur- tace moves upward when subjected to forces by a vertical tool At greater depths the degree of confinement increases to the point where soil moves laterally around the tool rather than toward the surface, i he studies of Kostritsyn were based on data obtained at a depth SOIL DTNAMICS IN TILLAGE AND TRACTION 199

~~TABLE ll.—Efect of the geometry of the soU-tool system on the cutting forces on a simple blade~~

~~Draft force required Depth of cut Geometry of Walls when width of cut was— (centi- cut cut meters) 22 cm. 39 cm. 90 cm. Kilo- Kilo- Kilo- Numl)er grams grams grams~~

~~3 300 325 530~~

~~270 480 7.5 — _ ■ 2 190~~

~~1 110 190 420~~

~~w/zw 3 700 740 — 550 15 0 "W/ZÁ 2 450 J//A 1 240 415~~

~~SOURCE: Zelenin {515).~~

where the surface influence did not exist. While these studies served a purpose, the need remains to examine the soil-tool relations near the surface where the variable boundary conditions exist. Zelenin attempted to explore the soil confinement along a vertical boundary that was essentially an open furrow wall ( 515 ). ^ata m table 13 show that the cutting resistance of the soil adjacent to the wall was considerably less than it was farther from the wall where the confinement was greater. Eegardless of the thickness, shape, or angle of operation of a tool, enough soil must be displaced to permit patsage. ^Consequently, for the conditions m table 13, c^tsjnade m excess of 35 centimeters from the wall required an ultimate cutting force of about 75 kilograms. The actual distance reflects the intlu- ence of geometric characteristics of the soil and the tool boundary and dyntmic behavior patterns of the soil. The distance from the open wall where the ultimate draft resistance is reached reflects the point where the total displacement or strain required to cause adequate failure is absorbed within the mass of the soil. At lesser distances from the wall, the soil is probably detached and moved into an open furrow as a rigid body in order to provide ™om for passage of the tool; hence, the forces required for displacement are reduced. Data are not available of side.forces on tools operating in these conditions but they should provide information that would be of assistance in evaluating the influence of geometry in such a ^^Nothini in Sie previous discussion implies that the specific strength of the soil was cliianged by the different soil-tool boundary conditions The change in draft of the tool was due to the different 200 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~TABLE IZ.—Influence of distance from a cutting wall on the cutting resistance of a simple tool 12 millimeters thick when operatinq in a vertical position~~

~~Distance from open wall Cutting (centimeters) resistance!~~

~~Kilograms 5 2.8 10 10.1 15 22.1 20 31.3 25 47.6 30 73.3 40 75.0 1 Cutting depth, 15 cm. SOURCE : Zelenin {515).~~

amounts of soil brought into failure. Different types of failure may also be caused by changes in the shape of a tool irrespective of the sou-tool boundary conditions. When a soil is strained by the passage of a tillage tool, the soil may react by compacting or by some type of failure that causes de- tachment ot the soil. When the soil is compacted, its strength may be increased and larger draft resistances of tools should result. Zelenin {515) conducted a series of experiments using cutters of dînèrent geometries to explore this type of situation. Figure 135 shows a series of tools used to cut soil. Notice that the degree of soil confinement is different for each tool. When the resistance of the soil IS not sufficient to immobilize the tool, the draft of the tool depends on the degree of coincidence between the direction of forces

~~URROW WALL~~

FIGURE 135.~Plan view of different soil-tool systems in which the soil reaction IS essentially the same. (Zelenin {515),) SOIL DYNAMICS IN TILLAGE AND TRACTION 201 applied by the movement of the tool and the direction of maximum resistance of the soil (table 14). The magnitude ^fd/i^f/^^^^^^f/ soil resistance arrows R (fig. 135) explam the magnitude of the cutting resistance that is measured. Thus, it has been demonstrated that the geometry of a tool is important even when the tool is operated near an open wall.

~~TABLE 1^.—Effect of geometry of an umymmetrical soil-tool system on the resistance of soil to cutting~~

Projected Cutting Cutting Type of Codei width resistance^ cutter angle of path Degrees Millimeters Kilograms 11.2 33.0 Symmetrical A 7.5 + 7.5 20 15.2 15.6 Unsymmetrical- B 24.0 C 25 19.0 Do 22.5 31.3 Do D 30 1 Shape of cutters is shown by designated letters in figure 135. 2 Tools operated 15 cm. deep in loam soil. SOURCE: Zelenin {515). Soil reactions associated with the overall orientation f too^^have been studied with simplified systems. Generally, mclmed planes have been forced through the soil to determine the force relations tVint nre associated with different tool orientations. SoTarîicS soil behavior has been characterized in these studies but th^e experimental data have been useful m both design and use cons deraSns. Figure 136 shows the influence of orientation on

~~95.9 Kg~~

~~70.0 Kg~~

~~45* 30« 30» 45» - ^^~~

~~" -45» -30' 0^ +30* +45* INCLINATION~~

Found. Engin. Procs., Butterworths, London (i67).) 202 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the maximum force required to move an underground plate (15 centimeters square) horizontally through the soil. The orientation was measured with respect to a plane perpendicular to the line of travel In each case the depth to which the top of the plate was initially buried was equal to the projected vertical height of the plate ( 187 ). Movement of the plate and maximum draft were accompanied by a simultaneous rupture of the soil surface. The nonagreement of draft torces between the inclined pairs of angles was apparently caused by the method of loading. The depth of operation was not maintained during measurement; hence, the plates that were inclined forward probably tended to slide upward into an area of lesser resistance even though movement was very slight. With the exception of certain underground cutting tools such as sweeps, most tools operated with a large portion of the tool having a surface-tool boundary. Vertical orientation of such tools has been studied more than lateral orientation ( 138, 322, 332, 398, 615 ). Simple tools have been observed and measured when they were swept back laterally {398), but theories have not been applied in an attempt to analyze their reactions. Kaburaki and Kisu ( 20A ) measured the influence of the lift angle a of a simple inclined tool when It was swept back laterally with a side angle ß. The projected area of the tool m the direction of travel was maintained rectangular and constant for all variations studied, and soil was moved laterally into an open furrow. The draft was influenced to a greater extent by the lift angle than by the side angle (fig. 137). The draft was

~~1.5~~

~~UJ o z 1.0~~

~~-L 10 20 30 40 50 60 70 80 90 CUTTING ANGLE ß (*>)~~

FIGURE 137.-Effect of the side angle on the draft of a simple inclined tool (Kaburaki and Kisu, Kanto-Tosan Agr. Expt. Sta. Jour. Uö^^ ) SOIL DYNAMICS IN TILLAGE AND TRACTION 203 essentially doubled when the lift angle was increased from 20° to 90°. Increases in the side angle ß decreased draft until an angle ot approximately 40° to 50° was attained. After that pomt, dratt became essentially constant for each value of a. In no case did the decrease in draft exceed 25 percent. For one special case, where a = ß = 45°, a parabolic increase in draft was found to be due to an increase in the width of cut regardless of the depth of cut. This relation has an important effect on the design and use of tools when optimum draft relations are of interest. The results of the influence of other orientations on the draft of a tool are shown m table 3b, where increases in the angle of approach result m increases m the draft force. This orientation is easily described m a simple tool system, but we shall see that much research is needed with regard to the orientation of tools having more complex shapes. When the main tillage action is cutting, the size of the isolated soil mass is determined by the size of cut of the tool. In a number ot cases, however, the final projected area of disturbed soil is not the same as the projected area of the tool. Because of this, tools may be located and oriented so that their sphere of influence includes all of the area to be tilled even though the tools do not intercept all ot the periphery. Kostritsyn ( 230 ) reported data of Dalm and Pav- lov, who measured the area of soil disturbance of small cylindrical tines (table 15). The data show that either soil bodies must form on tools or the arching effect in the soil results in a disturbed zone ot soil considerably larger than the projected area of the tool.

~~TABLE 15.—Sphere of influence of cylindrical tiries in soil~~

~~Diameter of tine Width of sphere of (millimeters) influence Millimeters 7.5 150 12.4 176 17.4 193 28.9 210~~

SOURCE : Kostritsyn ( ¡ Certain geometric characterizations of soil-tool systems have evolved as important indicators of soil-tool reactions. Included m this group are such characteristics as length-width ratios, depth- width ratios, and perimeter-area ratios. While these ratios are often dimensionless, they reflect the general nature of soil reactions. If a tool acts as a long narrow tool, it tends to cut the soil rather than to cause failure by shear. i i i. • Payne ( 329 ) has classed tines operating below an extended horizontal surface as being wide if the depth-width ratio exceeds 1.5. The ratio designates the portion of the tool that is m contact with the soil rather than the absolute dimensions of the tool. The 1.5 ratio apparently roughly determines the point where ih^ frontal portion of the crescent or shell just becomes flat, as shown in figure 138, B, Kaburaki and Kisu ( 20^ ) found that a minimum m the total draft force occurred for a vertical tool at a depth-width ratio of 0.5 (fig. 139, A), Measurements were made on small inclined tools 204 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~(A) (B) (C) FIGURE 138.—Action of tines, as evidenced by their characteristic soil reaoHnn •~~

~~(A) (B)~~

FIGURE 139.-Effect of depth-width ratios of simple tools on draft force (Kaburaki and Kisu, Kanto-Tosan Agr. Expt Sta. Jour ( Tof).) operating adjacent to an open furrow wall. The minimum became more pronounced as the area of the tool A increased. The length of the cutting perimeter was also minimum at this point. When the ofof° thehl^nir?'''''^«*^ cut (a = ^ = *^'jr*^'^^ 45°), a decreasing ^'^'^ ?^*^ ™depth-width"y t«^'^^d ratiothe open resulted side n a decrease m total draft. In this case a constant low value was at tamed so that a minimum as such did not occur (ñs 139 B) This fnlf îwï *^ ^°.- ^""í^ber of cases in which the profected'area of the i?ptU« *h.^, ^^^tical plane F was varied from 10 to 30 square centimeters. The wide ran^e of depth-width ratios through which this low value of draft resistance is found is indeed fortunate for de- fn^XT fi,"'®''!^^ "^oldboard plows; wide changes may be made the tool without increasing the specific draft of Geometric characterizations such as depth-width ratios cannot be SOIL DYNAMICS IN TILLAGE AND TRACTION 205 considered fundamental for describing tillage tools, since such parameters are meaningful only insofar as they represent the mterrela- tions of the soil-tool system. Figure 140 shows a soil reaction

~~mwrnim/u RUPTURE ZONE~~

~~TOOL~~

~~SOIL BODY~~

FIGURE 140.—SOU reaction to narrow, long tillage tools. (Zelenin (515).) characteristic of very long, narrow tools. Soil near the surface yields along the line of least resistance. Eathie ( S4ß ) placed layers of colored sand m his test sand media to serve as markers for the movement of soil by the tool. Excava- tion of the test media after tillage established the final position of the marker layers so that the soil reactions could be established Alter studying the soil body that formed on tools ranging from 15 to 100 millimeters in width, certain repetitive patterns could be established. In general, a horizontal section cut through the soil body showed tliat an essentially semicircular soil body was formed at moderate depths. The tool having a width of 100 millimeters and operating at a depth of 300 millimeters became completely enclosed in the soil body. At the surface, the soil body extended about 90 millimeters forward ot the cutter and had a maximum width of about 175 millimeters i his size tapered with depth to the bottom of the tool where the width was reduced to the width of the tool and the body extended forward a distance of 50 millimeters. In addition, a thin layer of soil (about 13 mm thick), formed on the bottom of the tool. Thus the tillage was performed by a body of soil, and movement occurred on a soil-soil rather than soil-tool interface. • v^ 4. A number of basic soil reactions that have resulted from difterent methods of force applications as controlled by the orientation ot the tool have been explored. As shown in this section, additional information is required before the specific forms of behavior can be defined to the point where they may be used m a rigorous mechanics. 4.5.4 Orientation of the Soil-Tool System The mechanics of soil-tool systems has generally been based on a simple coordinate system convenient for the experimental apparatus. As a result, little thought has been given to the influence ot the actual slope of terrain where a tool may be operated. The orientation of the soil-tool system cannot be considered as an abstract relation The orientation must be linked into some standard and well- established frame of reference. As a rule, orientation with respect 206 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE to the horizontal plane and the line of travel should be indicated since this will orient the direction of gravitational force. While the slope of terrain has been recognized as being important in vehicle studies (475), few quantitative studies have been made in coniunc- tion with tillage. Martini (293) studied the movement of soil caused by plows operated at different speeds and moving in different directions on a slope. Thus, while the soil-tool geometry was maintained constant, the overall orientation of the system was not. Since the influence of gravity and the direction of the forces applied by the plow varied considerably, the movement of soil differed for the different directions of travel. Figure 141 shows the displacement of the center of

~~SPEED 0.4 m/sec — — 1.6 m/sec~~

FIGURE 141.—The movement of the center of gravity S of SL plow furrow caused by plowing in different directions along a 15° slope at two speeds. (Martini Rocz. Nauk. Roln. ( 293 ). ) gravity /S' of a unit of the plow furrow slice when plowing was done on a 15° slope with a right-hand plow at two speeds. The initial location S is shown at the center of the direction rays. The final location of the center of gravity of the plow furrow is shown by S^j where n is the numbered direction in which the plow traveled. The experiment demonstrates a method by which the soil reaction was described in a simple quantitative manner. Since the minimum movement of the centroid of the soil mass represents the minimum expenditure of energy commensurate with the work accomplished, perhaps this technique can be used to partly evaluate the performance of plows. SOIL DYNAMICS IN TILLAGE AND TRACTION 207 4.5.5 Geometry of Interacting Tools The concept of a tool operating independently in a semi-infinite mass of soil is a physical unreality in actual tillage machmes. Until now, each tool has been discussed as being isolated. The mechanics of a combined tool system can be approached on a rationalized basis only when any interaction is identified and characterized. Little progress has been made in this direction except for general observations of interactions. In the development of a mechanics for interacting tools, the state of knowledge remains in the recognition stage (fig 76) and more qualitative information is required. The importance of interactions due to geometrical relations is discussed m chapter 5 in connection with design considerations. Kathie ( 3JÍ2 ) conducted studies concerning the interaction ot two vertical straight tools. The interactions of the soil reactions are illustrated in figure 142, where two tools may be visualized as op-

~~TOP VIEW~~

~~FRONT VIEW~~

~~^}&UW '>&/Mj^ ^pmr yjaM /\~~

~~(A) (B) (C)~~

~~FIGURE 142.—Interaction of the rupture zones of two UHage tools: ^» acting independently; i?, interacting; 0, essentially constituting a new tool of greater width.~~

crating with different degrees of interdependence. The importance of the geometry of the system is clearly evident, not only m terms of soil reaction but also in terms of draft force. The draft resistance of two tools, each 15 millimeters wide, was found to depend on the ratio of the distance between tools d and the depth of operation t. Wlien the tools were close together, a common compression wedge was formed similar to that in front of a single tool of the same overall width. When the tools were gradually moved apart, the resistance for a given depth increased and reached a maximum for the system where d = 0.043#. As the tools were moved farther apart, the compression wedge that had bridged over the gap between the two tools was broken through at the bottom and soil flowed between the two tools. The draft force dropped rapidly with an increase m the spacing between the tools and reached a minimum value when d = 0 34# At that point the draft force was only 10 percent higher than that of a single tool. As the distance between the tools was 208 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE increased still further, the draft increased until the point d = '2.6t was reached and the cutters were acting independently. Zelenin ( 515 ) repeated experiments of this type at several depths and found a similar relation (fig. 143). At the shallow depths, the

~~DEPTH (cm) 18~~

~~5 10 15 20 25 DISTANCE BETWEEN TOOLS (cm)~~

~~FIGURE 143.—Eftect on the draft force of the distance-of-spacing interaction between two simple vertical tools. (Zelenin ( 515 ).)~~

distance between tools at which the minimum draft occurred was only slightly influenced by the depth of operation. The minimum draft increased only from a point where the spacing between the tools was 5 centimeters to a point where the spacing between tools was 7 centimeters as the depth increased from 9 to 18 centimeters. Additional research is needed for tools operating at greater depths. Investigations such as those just discussed indicate the possibility of designing tools so that their maximum effective zone of influence (soil disturbance) will be commensurate with acceptable power requirements. The shape of the disturbed area is further complicated when the tools are not vertical. The shapes of areas disturbed by these types of tools have been studied by Payne and Tanner (382), and several examples of failure patterns are shown in figure 184. 4.5.6 Conclusions It is indeed unfortunate that observations of Jenkin (201 ) concerning the mechanics of tillage tools were not heeded at an early date. They might have guided research into more rigorous and profitable findings. Eathje (342) established the nature of soil reactions to tillage tools in 1932. In addition, he measured the stress distributions m the soil by means of pressure transducers. Love ( 256), on the other hand, developed a mathematical model for calculating stress distributions in 1929. Having read the work of Eathje and Love, Jenkin ( 201 ) wrote in 1932, 'The rounded shape of the 'Staukorper' or dead sand carried in the front of the cutter may be compared with the figures on page 419 of Professor Love's paper on The Stresses Produced in a Semi-Infinite Solid by Près- SOIL DYNAMICS IN TILLAGE AND TRACTION 209 sure on Part of the Boundary' * * *. These researches might well form a starting point for a research into ploughing, which is urgently- needed now that farming is being mechanized." Thus, the keen per- ception of this civil engineer led him to suggest a rigorous method by which to approach the mechanics of plowing. This is remmiscent of Van't Hoff, who associated Pfeffer's osmotic pressure with the fundamental aspects of the gas laws. Glasstone ( 153 ) has recorded the historical sequence of these developments. Attempts must be made to tie the physical system of the tillage tool into a known theoretical system or to devise a new theory for such a purpose. Chapter 4 was developed with this point in mind. 4.6 Mechanics of Complex Reactions The simplified actions discussed in section 4.3 could be represented with rudimentary forms of mechanics in which the various types of soil behavior were identified. Sufficient knowledge was available so that the simple behavior equations that were utilized represented a main segment of the total action that was of interest. As more and more complex soil reactions become of interest, additional forms of behavior will have to be considered. In some instances these specific forms of behavior are not available. Cutting as a soil separating action is not completely defined by any of the mechanics that have been discussed previously because its exact nature and importance have not been established. Soehne proposed ih^ use of a cutting term kl for roots but neglected it m his mechanics. Kawamura observed that the sharp edge of an inclined tool pried blocks of soil loose so that they failed along a line extending below the lowermost part of the tool ; obviously they were not cut loose. Kostritsyn neglected a frontal cutting component m his cutting mechanics. The question might then arise as to whether a pure cutting action of tools really exists in soil. The lack of definition of a pure cutting component and the nonrepetitive soil reaction might tend to support this contention. A closer examination of the available data, however, indicates that this point must be explored in greater detail before any final conclusion can be reached. The shapes of the curves for mean deformation Z«, and for resistance to deformation K^i (fig. 102) indicate that resistance increases in importance as the size of the cutter decreases. This also means that the percentage of total resistance on a long cutter face must reflect the same situation and that a relatively important component in the total resistance is associated with the tip of a cutter. This may be explained most easily when the size of the particles are large as contrasted to the thickness of the cutting edge. In this case the particles must be severed before the tool can pass. A unique situation may exist when the def ormability of the soil is low and a thick cutter enters the particle or clod. The large lateral strains may propagate a crack in front of the cutting edge so that the soil is torn apart just as a block of wood is split by an axe. , Marshall and Quirk ( 292 ) reported data obtained by cutting dit- ferent sizes of aggregates with a steel wedge-shaped cutter. They ^ound that the total cutting force was proportional to the size of the 210 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE aggregate but that the mean load per unit of active cutting edge was fairly constant for any given soil condition. Even with small aggregates (22, 8, and 3 mm.), failure occurred along the path of the cutter and not along natural cleavage surfaces. Thus, cutting is a directed action and the concentrated force causes a failure in the immediate vicinity of the tool so that other failures must be due to forces applied by other non cutting segments of the tool. The observation by Kawamura that the soil may fail below the cutting edge follows from the condition where deformation of the mass by a rearward portion of the tool strains the mass to a progressive failure at some point m front of the cutting edge. The total strain induced by the tool was not absorbed by the soil ; hence, the soil was displaced as a rigid body and the shear block formed. Not all shear blocks fail in this manner, and m some the edge did cut soil as the tool moved. Thus, conceivably, there will be instances where no continuous pure cutting action occurs since the soil may be intermittently torn apart by internal stresses or cleaved apart by a soil body which is formed on the tool. Kostritsyn's restriction of theory to the zone of the horizontal soil deformation in figure 96 does not imply that no cutting action IS taking place in the upper part of the soil profile. The action was neglected to simplify the definition of forces within the system he had undertaken to study. The mechanics of a complex reaction that includes cutting can be developed only when a pure component of cutting is envisioned and described m quantitative terms by a behavior equation. The pure cutting behavior equation must be included with shear, tension, friction, adhesion, and acceleration equations to form the mechanics. Until this IS done, the intermittent influence of cutting will cause discrepancies between measured and calculated values of performance. Complex reactions will be exceedingly difficult to describe by a mechanics. If the action to be described is simple, the mechanics will probably be simple since fewer behavior equations will be required. The mathematics of the mechanics must fit the observed action, or the incorporation of mathematical rigor into the mechanics will be of no avail. The principles discussed in section 4.2 should provide a means of developing the mechanics for complex tools. 5. DESIGN OF TILLAGE TOOLS

5.1 Introduction Tillage is the manipulation of soil by mechanical forces. The purpose of tillage tool design is to create a mechanical system, that is, a tillage machine or a series of machines capable of controllmg the applied forces in order to achieve a desired soil condition As a matter of definition, a tillage tool will be considered a single soil- working element whereas a tillage implement or machine will be considered a group of soil-working elements. A tillage implement or machine will include the frame, wheels, or other structural units that are needed for guidance and support. Although tillage is nearly always effected with an implement, the emphasis here will be on the design of tillage tools rather than implements. The pressing need for design information has demanded that methods for design be developed. In fact, the need is so great that qualitative procedures have been and still are widely used. The qualitative procedures have often been based on art rather than science (121, 269). That these procedures must be changed it progress is to be made in tillage tool design is clearly demonstrated by the history of tillage tools. , • -^ . Basic tools such as the forked stick date back into antiquity; yet, they are still found in their original form in many parts of the world. Even in more advanced societies, today, the moldboard plow is designed by empirical methods. Generally, these empirical methods are trial-and-error attempts; the tool is varied m some manner and acceptable designs are identified when the resulting soil condition is adjudged to be satisfactory. Quantitative descriptions or representations of the final soil condition are seldom used and, m addition, the forces required to move the tool are frequently not quantitatively assessed. Generally, no effort is made to describe the reaction of the soil. Consequently, design today merely accepts what occurs; it does not control what occurs. Thus, even though the need for design is great, design in the true sense of the word is not accomplished and probably will not be accomplished until quantitative information is available. . To illustrate the pressing need for design information, consider the economic possibilities of the results of better design. In the United States, more than 250 billion tons of soil are estimated to be stirred or turned each year (268). To plow this soil once requires 500 million gallons of gasoline costing $105 million. If proper design could decrease the draft of the plow only 1 percent, a savings in direct operating cost of $1 million per plowing would result. It soil manipulation can be controlled by proper design so that subsequent operations may be minimized or even eliminated, additional 211 212 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE savings would result. Control cannot be assigned realistic dollar values today because its economic effects are not known. The benefits of control in road building, land leveling, and plant growth, however, must be considered. 5.2 The Design Equations In tillage tool design, a limited number of abstract factors become of primary importance. In order to utilize the capability of soil for some specific purpose, the soil must be manipulated (changed, moved, or formed) to a desired condition. The manipulation is accomplished with a tillage tool by moving the tool through the soil. To obtain different final soil conditions, only the shape of the tool and the manner of moving the tool can be varied. Three abstract design factors define the manipulation: the initial soil conditions, the shape of the tillage tool, and the manner of moving the tool. The factors are abstract because each is not clearly defined in a quantitative sense although qualitatively they represent distinct and complete elements in tillage tool design. Two other design factors are important, namely, the forces required to move the tillage tool through the soil and the results of the manipulation— that it, the final soil conditions, unlike the other design factors, the forces can be quantitatively defined. Note that the forces are not those that are applied to the soil; they are those that must be applied to the tool to move it. The tool, in turn, applies equal but opposite forces to the soil. The five design factors represent the five elements that are of direct concern and, hence, of importance to a tillage tool designer. Eelations between the various design factors provide a means for designing a tillage tool. These relations can be qualitatively determined from available knowledge of the physical action of a tool that is manipulating soil. The concept of a mathematical function is useful in representing the relations. Two real variables are mathematically defined to be functionally related within some range if a definite single value of one of the real variables corresponds with a definite single value of the other variable according to some rule. The rule that prescribes the corresponding value is the functional relation. The concept can be extended to several variables. A functional relation exists if a definite single value for each independent variable corresponds to a definite single value for a dependent variable according to some rule. For example, if a dependent variable is a function of four independent variables, specifying the value of each of the four independent variables determines the value of the dependent variable. Consider the number of single value correspondence rules possible for the five design factors. If tool shape is physically varied but the manner of movement and the initial soil conditions are kept constant, the forces required to move the tool and the resulting soil conditions vary as tool shape is varied. Further- more, for each "value" of tool shape, a definite "value" of the forces and final soil condition exists. If a definite value does not exist, no unique law of nature exists. Available knowledge indicates that some kind of law does exist and tool shape does affect tool forces and SOIL DYNAMICS IN TILLAGE AND TRACTION 213 the resultant soil condition. Thus, in mathematical terms, shape, forces, and final soil condition are functionally related. Consider the situation where the tool shape and manner of movement are kept constant but soil conditions are physically varied. Available knowledge indicates that for each initial soil condition (a single "value"), definite tool forces are required and a definite final soil condition results. A functional relation between initial soil condition, tool forces, and resultant soil condition represents the situation. By similar reasoning, the manner of tool movement, tool forces, and resultant soil condition are also functionally related. Consider the possibility of physically varying tool forces for constant tool shape, manner of movement, and initial soil condition. Available knowledge indicates that in a constant initial soil condition, the forces cannot be varied unless tool shape or manner of movement is changed. If a tool is operated in a soil whose condition is constant and the tool forces are not sufficiently large, the tool cannot be moved. If the forces are too large, the tool will be accelerated or its path of movement changed. Tool shape, manner of movement, and the initial soil condition, therefore, completely determine the magnitude of the forces required to move the tool. In a similar manner, tool shape, manner of movement, and the initial soil condition completely determine the resultant soil condition. Mathematically, tool shape, manner of movement, and the initial soil condition are independent variables. The tool forces and resultant soil condition are each dependent variables, and they are mathematical functions of the same independent variables. The implied relation >^etween design factors is schematically represented in figure 144. The generalized tillage relation can be mathematically represented by the two equations F = f{Ts,Tm,S,), (132) Sf = g{Ts,Tm,S,), (133) where F — forces on the tool to cause movement, Ts = tool shape, Tm = manner of tool movement. Si — initial soil condition, / — functional relation between F^ Ts-, Tm^ Si, Sf — final soil condition, g = functional relation between A/, Ts^ Tm-, Si- The two equations—the force tillage equation and the soil condition tillage equation—represent the most general situation because, as written, the functional relations / and g are completely arbitrary. Furthermore, the two functions may or may not be different. The independence of the functional relations is of interest because of a possible higher order functional relation between F and Sf, If F and Sf are functionally related, equations 132 and 133 can be combined so that the relation between the design variables is represented by only one equation. Available knowledge does not conclusively indicate whether F and Sf should be related. The possibility thus exists that two separate equations inaccurately represent the generalized relations between the design factors. Available mathematical 214 AGRICULTURE HANDBOOK 316, U.S. DBPT. OF AGRICULTURE

~~INITIAL SOIL CONDITION FINAL ^í;;íííí;.soiLí;íí;ir;rí SOIL CONDITION TOOL SHAPE »^;',MANIPULATION;í;; TOOL FORCES TOOL MOVEMENT mmmm~~

~~FIGURE 144.—Relation between soil and tool factors in design.~~

knowledge helps to resolve the situation. Available mathematical theorems prove that F and 8f will be related only if the nature of / and p' is such that their Jacobian is zero. Furthermore, the mathematics provides a means for determining the higher order relation if it exists. Thus, no mathematical restrictions are imposed on the possible functional relations if two equations are used. Two equations actually simplify the situation since each can be studied independently, although physically both equations operate simultaneously. Available knowledge assures that F and Sf are both dependent variables of the same independent variables. Equations 132 and 133 represent that knowledge. The general relation between the five design factors is, therefore, accurately represented bv equations 132 and 133. ^ A study of the design factors and of the relations between them represent a change in our scope of interest. In chapters 2, 3, and 4 our attention was concentrated only on what happens to soil when it IS subjected to dominant force systems. Intuition, observation, and experience all indicate that dominant forces cause and control manipulation of soil. Our scope of interest thus was concerned with quantitatively describing the reaction of soil to forces, and forces and soil behavior were of primary importance. When designing a tillage tool for the purpose of establishing a new soil condition, our interest is no longer concentrated on the dynamic progress of the reaction of soil per se but rather on a soil- tillage tool system and on the results of the reaction—the final soil condition. In design, an accurate description of how soil reacts is not essential. But the results of the reaction and what can be done to control the reaction are essential. Therefore, for design, our scope of interest must be concentrated on a quantitative description of the final soil condition and on how the manipulation can be controlled. The design factors and their relations indicated by equations 132 and 133 represent the desired quantitative descriptions for a scope of interest concerned with design. The circle (fig. 144) hypothetically illustrates a change in our SOIL DYNAMICS IN TILLAGE AND TRACTION 215 scope of interest. Inside the circle, the soil may be visualized as being manipulated. Forces cause the manipulation, so our scope of interest centers on describing the reaction of soil to forces. Out- side the circle, the results of the final soil condition and the control of the manipulation are of primary concern. The design scope of interest is thus represented by quantities operating outside the circle. The relation between the two scopes of interest was implied in section 4.2.2; more is said concerning their relation later in this section. The procedural framework for designing a tillage tool is contained in equations 132 and 133. Knowledge of the functions represented in the equations would permit a designer to use equation 133 to determine the resulting soil condition and equation 132 to determine the forces required to move the tillage tool. By simultaneously considering both equations, the possible tool shapes and movements could be optimized to effect the desired manipulation with minimum force. Since the functions are not yet known, the equations cannot be used directly for design. Even in their generalized functional form, however, they inherently establish guidelines for empirical design procedures. The total differential of equation 132 is

~~als 01 m 0^>i and similarly the total differential of equation 133 is~~

dSf = ^ dTs + jf dT,, + ^ dS„ (135) ' dis olni OK>i Equations IM and 135 give the reasoning behind qualitative design procedures. For example, the shape of a tillage tool can be varied and the tool in each of its various shapes can be operated in a soil of uniform condition. If the movement of the tool is not changed (depth, width, speed, etc.), any change in the forces required to move the tool or any change in the results of the manipulation must come from the change in its shape. The conclusion is valid because equations 134 and 135 become, respectively,

~~dF = (S-) dTs, (136) \0l s /Tm,Si dS, = (-If) dT,, (137)~~

since dTm and dSi are both zero for the conditions of the observations. If one particular shape produces a soil manipulation that is judged to be superior, a description of that shape provides useful design information. Only the shape would need to be quantitatively described; the forces and the resulting soil change would not. The tool with the selected shape could be operated in various soil conditions to verify its action. If the required forces and the resultant soil manipulation were judged satisfactory, it could be concluded that the selected shape is an acceptable design for these soil conditions. Describing the soil conditions even in qualitative terms pro- 216 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE vides additional design information that can be associated with the description of the shape. Such procedures have led to the development of sod bottoms, general purpose bottoms, and slat bottoms for moldboard plows. The procedures were qualitative because numerical descriptions of all of the design factors were not necessarily used and no attempt was made to relate the design factors. Quantitative design procedures involve numerically relating the design factors to each other. If F and T^ are measured (numerically assessed) in circumstances that are accurately represented by equation 136, a unique relation between F and T^ must exist. The relation can be represented graphically by plotting the variables against each other. The plot results in a curve that represents the relation, and the equation for the curve is the solution of the differential equation in equation 136. The relation between 8^ and T^ could be developed in a similar manner. Eepeating the measurements in different soil conditions results in the development of a family of curves with each curve representing a constant soil condition. If the soil conditions are quantitatively described, relations between F and 8% and Sf and Si for constant tool shape can be obtained. The equations that describe the relations provide the solutions to equations 134 and 135 when only the soil is varied. In a similar manner, tool movement can be varied when tool shape and initial soil conditions are constant to again provide equations to describe the indicated relations. Conceivably, all of these equations could be simultaneously considered or combined so that ultimately equations 132 and 133 could be developed. Quantitative design procedures, therefore, can lead to the development of the functions / and g in the tillage equations. A system of soil and tool description equations such as discussed in section 4.2.2 can be shown to provide the means to derive a tillage equation. A certain group of tillage tools can be described geo- metrically by one equation or more. For example, all disks made from sections of spheres can be described by the equation for a sphere. The radius of the sphere and the limits that describe the section of the sphere from which the disk is made (diameter of the disk) become parameters of the geometrical description equations. Specifying a particular disk fixes the parameters of geometrical description equations just as specifying a particular soil condition fixes the parameters of dynamic property equations. The system of equations forms a mechanics, and the solution of the system of equations can be obtained in terms of the parameters of both the soil (dynamic parameters) and the tool (geometrical parameters). The solution will be a tillage equation. From such a generalized solution, the effects of varying either the soil conditions for a specific tool or the tool for a fixed soil condition could be determined. Another possible application of a general solution would be to consider only one specific tool. The path of motion could be expressed by equations, then mathematically varied, and the results determined. An elementary example of this approach would be in varying width and depth of operation. A generalized solution of the system of equations in terms of the parameters of soil (dynamic parameters) and path of motion parameters thus provides another tillage equation. In this instance the effects of varying either the SOIL DYNAMICS IN TILLAGE AND TRACTION 217 soil path in fixed soil conditions or the soil conditions for á fixed soil path could be determined. The general procedure described here provides a means for determining tillage equations to form a soil- tillage tool mechanics. Two approaches for developing the tillage equations have been discussed. The approach based on experimental observation is empirical. Calculating the equations in the manner discussed in section 4.2.2 is not empirical ; it is derived. The tillage equations are based on behavior equations, and each behavior equation represents a scientific principle. One might justifiably argue that each behavior equation is itself empirical. Such is the case unless each principle behavior equation is calculated from subbehavior equations. In reality, every behavior equation probably is empirical at some period of its development. Once the relation has been verified and is accepted, it may be called a law and hence represents a scientific principle. Any action that is described by equations developed from established principle-behavior equations is not empirical. An action that is described by equations developed from experimental observation, however, is empirical. Several examples of equations based on empirical observations and also based on scientific principles exist. Charles and Boyles' Laws, which are concerned with the behavior of confined gases, were empirically developed. Kinetic Theory and Statistical Mechanics were developed later, and both provide principles and methods that permit calculating the empirical gas laws. Kepler's Laws of Motion were based on observation, and they describe the motions of the planets about the sun. Newton's Law of Gravitation provides a single principle behavior equation that permits calculating Kepler s Laws of Motion. Many other examples could be given. If both the empirical and the derived approaches have been fully developed, the descriptions of an action will not differ in accuracy. In fact, an empirical development and a derived development could lead to the same equation. On the other hand, different but equally accurate equations could be developed because, as was discussed in section 4.2.1, no unique organized system of behavior equations exists. The important difference between the empirical and derived approaches is their intrinsic understanding. Empirical equations can describe only the action. While the description may be accurate, no knowledge is inherent in the description as to how or why the action occurs. Kepler's Laws of Motion are accurate, but Newton]s Law of Gravitation explains why planets move as they do. Simi- larly, Kinetic Theory explains how and why the behavior of many individual gas molecules create the pressure volume relations described by Charles and Boyles' Laws. The questions how and why can be answered only when principal and even subordinate behaviors have been isolated, identified, quantitatively described, and finally combined into a mechanics to represent an action. Since many design equations must exist, a technique for representing a design factor may aid in developing tillage equations. Recall that behavior equations were said to contain parameters, and these parameters assessed the contribution of the material to the behavior. In a similar manner, parameters of tillage equations can be used to represent one of the independent design factors. 218 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE To illustrate the technique, consider a situation where equation 136 is applicable. Assume that a relation between F and T^ is experimentally obtained and is graphically represented. The resulting curve represents the relation between F and T^ at a constant soil condition and a constant manner of miovement. If the measurements are repeated in a different soil condition the resulting curve probably will be different. By repeating the measurements in several soil conditions, a series of curves can be developed. The difference between curves reflects the difference between initial soil conditions. Assume that the curves are all similar and that an equation can be developed that represents \h^ curves. The equation that describes all of the curves can be said to be a general equation. To be a general equation, rather than a specific equation, it must contain parameters. These parameters will numerically assess the initial soil condition. For example, if the relation between F and T^ is linear, the intercept and slope are parameters of the equation and they would numerically assess S^ in the tillage equation. Each different soil condition will have a different slope and intercept. If the manner of tool movement were changed, rather than initial soil conditions, a different family of curves would result. Developing a general equation to represent the curves again will define parameters. In this case they will assess the manner of movement rather than the initial soil condition. In short, the technique provides a means to numerically define and assess one of the independent variables in the tillage equation. The technique has one serious limitation. Just as behavior equations define behavior parameters so tillage equations define design parameters. Consequently, the design parameters are defined by the soil-tillage tool system. In order to assess the parameters, a particular tool must be physically operated in a manner that simulates the system being represented. Once the parameters have been assessed, all similar tools can be described by the equations. The situation IS exactly analogous to the cutting parameters discussed in section 4.3.2. The cutting parameters were defined by the mechanics of cutting rather than by a behavior equation. The limitation could possibly be minimized if the design parameters could be related to some other defined factor in the system. For example, if the design parameters assess the soil, they must be determined by the material and state properties of the soil just as dynamic behavior parameters must be determined by these same soil properties. Establishing the relation would overcome the limitation of the technique. The need for design information and the complexity of the relations involved between the design factors clearly indicate that both the empirical approach and the derived approach should be simultaneously followed. Each approach requires certain facilities and interests. The empirical approach requires facilities for keeping soil condition constant and for producing various shapes of tools and equipment for controlling the manner of movement. As equations 134 and 135 indicate, control must be sufficient so that any change m F or 8f can be attributed to the correct design factor. In the derived approach, soil behavior can often be studied with small samples of soil and rather simple apparatus. A mechanics based on behavior eiquations can be developed with only a pencil and paper. Facilities SOIL DYNAMICS IN TILLAGE AND TRACTION 219 and personal interest, therefore, should partly determine the approach to follow. In the empirical approach, however, emphasis must be placed on establishing quantitative relations. Only when design information must be immediately available should qualitative empirical procedures be followed. Qualitative procedures can never lead to the information needed for design where control of soil manipulation is possible. Finally, one should recognize that a complete understanding of the general behavior of soil reacting to a tillage tool can be obtained only from knowledge based on scientific principles. Such principles can never be deduced from an empirical description of general behavior. Therefore, the derived approach will ultimately have to be fully developed before a complete understanding of the soil-tillage tool system can be attained. 5.3 Shape Of the three design factors incorporated in equations 132 and 133 (shape, manner of movement, and the initial soil condition), the designer has complete control only over shape. The user of a tillage tool may vary the depth or speed of operation and may use the tool through a wide range of initial soil conditions. The shape of tillage tools, therefore, has received considerable emphasis since the ideal tillage tool should perform satisfactorily over wide ranges of soil conditions and depths and speeds of operation. Tool shape cannot be considered independently of its manner of movement or the initial soil condition. A description of tool shape must also be oriented with respect to the direction of travel of the tool, or its operating geometry will be ill defined. Likewise, different initial soil conditions sometimes require different shapes. This situation has resulted in the development of various configurations of moldboard plows for different soils and conditions. Since shape is the only design factor over which the designer has complete control, it must be given primary consideration in tool design. When considering shape as a design factor, one of the first steps is to describe the shape of a tool. A description is required for the design equations as well as for construction purposes. Many tillage tools have complex shapes, and these shapes cannot easily be represented in mathematical form. Therefore, the shape description of a tool is almost exclusively restricted to the surface that comes in direct contact with the soil. Generally, no attempt is made to represent other surfaces of the tool mathematically, except when clearance is required to prevent undesirable contact with the soil. A mathematical description of the shape of a tool is the most versatile means of representation. For some simple shapes, a plane adequately represents the surface ; and the plane along with its orientation is relatively easy to describe mathematically. As more complex surfaces have evolved, however, standard mathematical equations often no longer represent the surfaces. Attempts have thus been made to find other ways to describe the complex shapes. These attempts often employed graphic representations of shapes that cannot easily be represented by mathematical equations. Some representations of tool shapes have been carried to the extreme so that the shape is described only by the pattern or mold used in its manufacture. The development of means to adequately describe the shape 220 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE of tillage tools is still a major area of concern in the design of tillage tools. A second step associated with shape as a design factor requires identification of the variables that represent the shape design factor Ts in equations 132 and 133. A third step is the establishment of the equations themselves. Unfortunately, these last two steps may have to be combined. To illustrate, the"^ shape variables in the design equations should be the parameters that are identified by mathematical descriptions of shape. Probably, however, geometric parameters will not be independent of each other in the design equations. Any dependence must be represented in the functional relation and the design equations will not be simple. On the other hand, a transition equation might be developed in which the shape description parameters are combined to define new variables that will be independent in the design equations. With independent variables, the design equations should be simpler and easier to develop. Thus, identifying the variables and developing the equations may not be separate. In essence they are separate, since independent variables could be identified ; but the functional relations could be so complex that they could not be established. Describing the shape, identifying the shape variables in the design equations, and developing the equations themselves are the three elements involved with shape as a design factor. 5.3.1 Soil Loosening and Turning Tools Tillage tools apply dominant forces to soil and cause the soil to yield in such a manner that it usually results in a loosening or turnmg of the soil. Although these actions usually are the intended purpose of tillage, they are involved any time a tool is moved through the soil regardless of the intent. Loosening and turning tools thus comprise a large category of soil manipulating tools. As a group, soil loosening and turning tools are widely used in agriculture. In 1925, approximately 28 percent of all energy expended on farms in the United States was used to operate soil loosening or turning tools. In 1961, approximately 60 percent of the tractor power that was utilized on farms was expended for comparable operations, and required more than 2 billion gallons of fuel costing $323 million. These figures do not include the energy used to operate planting equipment, which also does a certain amount of turnmg. The figures do show not only the economic importance of the group of tools but also the reason for emphasis on equation 132 of the design equations. The forces are directly involved in the energy required to operate the tillage tools. When human and animal power were used to operate tillage tools, the limiting factor in tillage was available power. Emphasis had to be on getting the job done as long as the resulting manipulation was satisfactory even though it was not controlled. Only with the advent of mechanization and the high-powered modern tractor has available power not been the dominating factor in tillage. Even where power is not limited, economic importance still brings pressure to bear on minimizing forces required to operate the soil loosening and turning tools. In the following sections we shall see that available information SOIL DYNAMICS IN TILLAGE AND TRACTION 221 concerned with shape has been concentrated on describing the shape. Only qualitative design information concerning shape is available in equations 132 or 133. 5.3.T.7 Macroshape The surface over which soil moves as a tillage tool is operated constitutes the shape that is of concern in design. Any finite surface has a boundary or edge whose "shape" is independent of the shape of the surface itself. A tillage tool is finite and has boundaries that are generally referred to as edges. The shape of edges in contact with soil affects the forces required for soil manipulation just as does the shape of the finite surface. Since the area of the edges of a tool is generally much smaller than the area of the surface itself, the term edgeshape is used to refer to the shape of edges while the term macroshape is used to designate and emphasize the shape of the gross surface. The moldboard plow is perhaps the most widely used tillage tool today. Its ancestor is, of course, the forked stick. While its history is long, descriptions of the macrosurface of a moldboard plow did not receive much emphasis until metals were used to construct the plow. Even then, the first descriptions of the surface were developed so that the plow could be constructed. Very little emphasis was placed on determining a relation between force and shape or between soil condition and shape that could be used to evaluate designs. Any emphasis that was placed on design resulted in information that could be utilized in equations 132 and 133 only in a qualitative sense {160), The usefulness of descriptions of shape, however, does not hinge on their utilization in design equations, since the first requirement in shape design is a description. One of the first methods for accurately describing the surface of a moldboard plow was developed by Thomas Jefferson in 1788 {199), It was a physical method that could be used for constructing a plow. A description was inherent in the method he proposed since it involved generating a surface with a rigid framework (fig. 145). The

FIGURE 145.—Jefferson's framework for designing a moldboard plow, (Jeff er- son, Proc. London Philos. Soc. { 199 ). 222 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE surface was generated by using lines e-m and o-h as directrixes and by moving a straight edge from g-e to m-h in such a manner that the straight edge remained and rotated within the vz plane. The surface generated by the straight edge as it moved was considered to be the surface that would invert the soil with the least possible resistance. Jefferson did not determine the mathematical description of the surface ; he merely devised the framework and the method of its use to represent a plow surface. A number of models of this type of framework have been used in constructmg moldboard plows. Whereas Jefferson used straight lines to represent both the generator (the moving line) and the directrixes (fixed lines), others have used catenaries, arcs of circles, cycloids, and helices. Never has the choice been based on more than intuition. The method does, however, provide a means of generating a vast number of different surfaces applicable to moldboard plows. A mathematical analysis of a surface generated by this method can be made to determine an equation that describes the surface. White ( 502, 503 ) analyzed a number of plows, including the Jeffer- sonian plow. He established equations for the surface in a cartesian coordinate system oriented as shown in figure 145. The surface equations were derived from the equations of three different lines that were passed through the surface. Upon a rotation of the reference coordinate system, the equations of the Jeffersonian plow could be reduced to those of hyperbolic paraboloids. White was able to obtain equations to describe other plow surfaces that were not hyperbolic paraboloids. He was unable, however, to relate these equations to either the forces or the resultant soil condition except in a general qualitative way. Nevertheless, his work is of merit because he demonstrated that an existing plow shape could be mathematically represented. Graphical descriptions of shape have been used by various researchers including White ( 502, 503 ), Ashby ( 18,19 ) and Krutikov and others {231), They used graphical methods both to describe the shape and to try to establish design equations. In one commonly used method for graphically determining macroshape, an apparatus similar to that shown in figure 146 is employed. The gridded plane on the right in figure 146 is used to position a measuring rod. The tool whose shape is to be described can be oriented so that the gridded plane represents a plane perpendicular to the direction of travel of the tool. If the gridded plane is a yz plane, the œ and y axes are so oriented that the xy plane is a horizontal plane and the xz plane is a vertical plane ; both contain the direction of travel. To describe the shape of a properly oriented tool, the distance x that the rod extends through the yz plane is recorded at each grid location in the yz plane. A two-dimensional graph can be made by plotting the x and y values at a constant z and by connecting the plotted points with a smooth curve. The curve represents the intersection of a horizontal plane and the surface being described. By superimposing a series of such contour lines m one plane and connecting the ends of the contour lines (the edges of the surface), a two-dimensional representation of the surface is constructed. SOIL DYNAMICS IN TILLAGE AND TRACTION 223

~~FiouKE 146.—An apparatus for describing the macroshape of tillage tools.~~

Representations of moldboard plow surfaces prepared by this method are sliown in figure 147. Soehne ( 40^, ^03 ) used an optical means to expedite the preparation of descriptions by this procedure. He projected a slit of light onto moldboard plows that were painted white and recorded the reflected light trace photographically. The technique provides a rapid and accurate means of obtaining descriptions of shape (fig. 148). The slit of light could be projected either vertically or horizontally so that contours could be obtained in either direction. Accuracy was assured since both the projector and the camera were fixed and only the plow bottom moved. Soehne labeled the photograph contours alphabetically from the bottom to the top and from the front to the rear, as shown in figure 149. Contour representations of the type shown in figures 147 and 149 generally have not been mathematically described. They have been useful, however, for comparing shapes and for manufacturing purposes.

~~■ ■ ■—I i »—I »~~

~~(A)~~

~~FIGURE 147.—Contour descriptions of two moldboard plows. (Reed, Agr. Agr. Engin. (350 ).) 224 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE~~

~~SLIT LIGHT PROJECTOR~~

~~CAMERA~~

~~FIGURE 148.—Arrangement for photographically recording the shape of tillage tools. ( Soehne, Grundlagen der Landtechnik ( Jf02 ). )~~

~~(A)~~

~~i*P^o I 1 \f\oc///y/' 4^.0 y \j^/v/ y\y Jl^/y^y / X ■ú^^i^ /i A. X ^yyx^ / / ' ^ ^^^^ //~~

~~1 ^ "^y^ \/^ X ^^^ \ \ / \ \*'5LÍ! ^^/^ b ■^/l^r\o ^ 1 \\ V~~

~~(B)~~

FIGURE 149.—Graphical representation of plow macroshape : A, Projections into a vertical plane of vertical contour lines formed by the intersection of the moldboard surface and a vertical slit of light; B, projections into a horizontal plane of horizontal contour lines formed by the intersection of the moldboard surface and a horizontal slit of light. ( Soehne, Grundlagen der Landtechnik ( ^ö^ ).) SOIL DYNAMICS IN TILLAGE AND TRACTION 225 One of the first attempts to relate shape to newly created soil conditions (equation 133) was made by Ashby (19), He utilized graphical representations from which he defined parameters ot the shape of plow bottoms. He attempted to correlate the shape parameters with observations of plow performance. His measure ot performance was primarily the covering of plant residues during actual plowing. Ashby defined a slope coefficient that was identified with the "full cut section" of a plow (fig. 150). This section is

~~FURROW WALL~~

~~FIGURE 150.—Ashby's "fuU cut section" (A—B) of moldboard plow. (Ashby (19).)~~

located in a vertical plane drawn perpendicular to the cutting edge of the share. The vertical plane is drawn to intersect the share at a distance from the furrow wall equal to the width of cut of the plow. The intersection of the plow surface and the vertical plane forms a curved line AB, which is used to define the slope coefficient. The curved line is shown in profile in figure 151, A along with its

~~"I D' > 7 i t~~

~~(A) (B)~~

FIGURE 151—A, Profile of fuU cut section of plow; B, profile of twist section of plow. (Ashby (19).) ' 226 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE projected distances ¿7, H, and X. Ashby defined the slope coefficient as follows: TJ Slope coefficient = xT2C^' ^^^"^^ where H - height of the plow, X — projected width of the plow, C - distance the top of mohiboard departs from the vertical line tangent to the curved profile. When the moldboard has considerable twist, the slope coefficient has to be modified by a correction factor. Another section of the plow, identified as the twist section DC in figure 150, lies parallel to the full cut section but is two-thirds of the distance from the full cut section to the wing tip. The profile of the twist section CD^ shown m figure 151, 5, was used to determine the slope coefficient correction factor. The correction factor was computed from the equation

~~Correction factor = (-^-0.20^ ^~^^"^^, (139)~~

where TF, 7, E, and Hjy are distances identified in figure 151, B, The correction factor was applied only when the ratio E/V was greater than 0.20. The slope coefficient as modified by equation 139 thus becomes

Slope coefficient - ^^-(.^-o.2o) ^~^^ + ^. (140) Ashby used equation 140 to calculate the slope coefficient of a number of moldboard plows. The plows were operated in a series of field experiments during which the covering performance of the plows was judged according to a standardized rating system. A multiple correlation was made between the covering performance and the number of plow shape factors believed to affect the covering performance. The correlation resulted in the following equation: X = 0M65A - 0.055^ - 0.644(7 - 0.118Z> - 0.0357^ + 4.072, (141) where X = subjective rating of covering performance, A = size of the plow, B = horizontal clearance of the plow, O = slope coefficient, D = width of plow at waist, E = relation of height to width of wing. As the regression coefficient in equation 141 indicates, the slope coefficient G appears to be the most important factor considered. Ashby's work illustrates one of the principles discussed in the empirical development of design equations. A parameter of the shape description is used as a variable in a design equation. Al- though this particular slope coefficient is probably a poor parameter and inadequately reflects the shape, it nevertheless is commendable SOIL DYNAMICS IN TILLAGE AND TRACTION 227 as a first attempt. One hopes that more than covering can be included as a measure of the newly created soil condition. In addition, a quantitative description of the covering should be developed to replace the standardized rating system. Although equation 141 is inadequate and probably inaccurate in terms of design needs for today, its weakness should serve as an impetus to seek improvement. In principle this rudimentary equation demonstrates that design equations can be developed. Soehne ( 402^ ^03 ) defined a number of parameters of shape descriptions and attempted to relate them to plow performance. He used the light slit technique to represent shape along grid lines 1-11 and a-m, spaced 40 millimeters apart (fig. 149). And he selected the following angles as parameters: = share cutting angle, <}>10a to (^lOj - lateral directional angle of the moldboard upper edge, 5a to

~~1.75 mph 7.75 mph~~

FIGURE 152.—The sou sliding path at two speeds of plow operation. (Soehne, Grundlagen der Landtechnik ( 1^02 ).) hour than at 1.75 miles per hour. The path of travel is related to the acceleration that is imparted to the soil ; this, in turn, affects the acceleration force that contributes to draft. After examining a number of plows, Soehne concluded that so-called high-speed plows accelerated the soil less than did so-called standard-speed plows. Carlson ( 60 ) reached the same conclusion from a study of two plow shapes in which he used a digital computer to calculate the acceleration characteristics of each shape. Even though the mathematical representation of acceleration is simple and fully developed, acceleration has not been quantitatively incorporated into design. Nichols and Kummer ( 319 ) developed a tracing apparatus that could provide empirical equations to describe the path of soil movement over a moldboard plow (fig. 153). The principle of the apparatus was similar to that of Jefferson {199)', he used a predetermined physical path along which to establish plow shape. The apparatus of Nichols and Kummer used the plow shape as the "directrix" to determine the orientation of the generator. Kecall that Jefferson prescribed the orientation of the generator which thus swept out the shape. The tracing method was based on the observation that most plow shapes represent a section of cylindrical surface. Therefore, a selected test arc may be fitted to the surface of a plow and swept across the plow along a hypothetical path of travel. As shown in figure 153, a measurement carriage rolling on guiding rails permits the test arc to be moved along the plow. At various increments of travel, which can also be considered to be units of time, the rotation SOIL DYNAMICS IN TILLAGE AND TRACTION 229

~~ARC~~

~~ROTATION ANGLES.~~

~~FIGURE 153.—Apparatus for tracing the path of soil movements and the shape of moldboard plows. (After Nichols and Kummer, Agr. Engin. { 319 ).)~~

angles (f) and 0 can be simultaneously measured. The variations m the vertical and horizontal rotation angles were plotted as functions of the carriage movement distance. The results combined cartesian and polar coordinates into a single graphical system that could be used to compare different plow shapes. A mathematical expression for the functional relation provides a description of shape. Al- though mathematical characterization of the curves indicates differences between shapes, the characterization provides no rigorous information that can be utilized in plow design. In spite of this lack of design information, the device established a physical link between soil and plow because the path measured by the device and the actual paths of soil moved by the standard speed plows used at that time fortuitously coincided. -,. , , T«. . Pfost (334), using the same apparatus m a slightly different fashion, simplified the procedures. He described the path of only one point at a radial distance R (fig. 153), whereas the horizontal rotational angle (f> was maintained perpendicular to the direction of travel. Only the values of the inversion angle 0 were recorded for each increment of S. As shown in figure 154, the constructed and the actual paths of soil travel for two plows agreed very well for one speed of plowing. Unfortunately, the speed at which the lines agree cannot be predicted, so that the usefulness of the method is limited to a descriptive role. Thus, while a description of actual path of soil travel is useful for calculating acceleration imparted to soil during movement over the surface, the description per se is no more useful for design purposes than a geometric description. Eegardless of the means by which macroshape is described, the description must ultimately be related quantitatively to forces and 230 AGRICULTURE HANDBOOK 316, U.S. DEPT. OP AGRICULTURE

~~100 -~~

~~CALCULATED VALUE c^--o MEASURED VALUE~~

~~20 30 40 S (cm)~~

~~FIGURE 154.—Constructed and actual paths of soil movement on moldboard plows. (Pfost, Auburn Univ. {334).)~~

final soil conditions as implied by equations 132 and 133. Until such relations are effected, quantitative design information will have to originate from trial-and-error procedures. Gross descriptions of shape, even though nondetailed, can be useful for design. Qualitative descriptions such as can be developed by the Jeffersonian technique have contributed greatly to the development of moldboard plows. The "use of one such gross description was reported by Kaburaki and Kisu (205), Modifications made in the shape of moldboard-type plows have resulted in better scouring characteristics for Japanese conditions. These developments have led to an elliptical-shaped plow (fig. 155). The exact nature of the superior f rictional relations was not determined ; but the tool had a smaller width of cut, which may have produced lower normal forces. Even though the design relations have not been established, the elliptical description permits a convenient shape characterization. Since the tool is symmetrical, it could also serve as a two-way plow, as shown in figure 155. Moldboard plows are the most widely used soil loosening and turning tools, but subsoilers require the largest draft force to move them through the soil. Thus, it is not surprising that the force-shape relation has received emphasis in subsoiler studies whereas the manipulation-shape relation has received emphasis in studies of the moldboard plow. The large draft requirement of subsoilers is the dominant characteristic that determines the extent to which it can be operated. Thus, the extent of soil breakup is of secondary importance, even though it is the reason for operating the subsoiler. Nichols and Eeaves ( S£2 ) measured the draft of a series of subsoilers with macroshapes that ranged from the normal straight configuration to a deeply curved configuration (fig. 156). Draft was measured in several soil conditions, and the results indicated that SOIL DYNAMICS IN TILLAGE AND TRACTION 231

~~/ /Í'AW/'A*, /^î^^^~~

~~SIDE VIEW FRONT VIEW~~

~~FIGURE 155.—An elliptical-shaped moldboard plow.~~

~~FIGURE 156.—Experimental curved subsoilers. (Nichols and Reaves, Agr. Engin. (322 ).)~~

the subsoiler with the most curve required the least draft (table 16). In a highly compacted and cohesive soil the curved tool required from 7 to 20 percent less draft than did the straight tool Ihis decrease is substantial, and crude observations indicated tlmt the resultant soil breakup was approximately the same tor all tool shapes The curved subsoiler presented an operational ditticulty, however, since its greater length made turning and guiding the tool while it was in the ground difficult. Xo effort was made to describe the shape or to relate shape to draft except in the qualitative manner indicated in table 16. ,. , i i *,. Improper operation can defeat the advantage of decreased draft with a curved subsoiler. Unless the curved tool is operated at its intended depth, all advantages of the curve may be lost. Presum- ably, the curved subsoiler gains its advantage from the direction in which it applies forces to the soil and the direction in which these forces cause the soil to move (fig. 157). The advantage of the proper use of the design ( fig. 157, A ) is lost if operation is too deep; 232 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~TABLE 1^.—Effect of shape on the draft of mhsoilers operating at a depth of 12 inches and a speed of i% miles per hour in various soils~~

Draft force Reduction in Soil type Straight Curved draft due to subsoiler subsoiler curved shape Pounds Pounds Percent Hiwassee sandy loam 890 890 0 Davidson clay __ __ _ 930 860 7.5 Decatur silty clay loam__ 1,825 1,415 22.4 Sharkey silty clay 2,000 1,820 9.0 Hurricane clay _ _ _ 2,120 1,820 14.2 Houston clay_ __ _ _ 2,040 1,660 18.5 SOURCE : Nichols and Reaves (, ).

the curved subsoiler operates as though it were straight (fig. 157, B), Figure 157, G depicts an obvious solution by design if operation at deeper depth is required. 5.3.7.2 Microshape and Friction Soil slides over the surfaces of tools which, as we have seen, may be described by the macroshape. Clearly, friction between the soil and the surface must be present so that two identical shapes could produce different results because of different soil-metal frictional relations at the interface. Consequently, the microshape on the surface may influence shape-design relations. Surface roughness caused by rust, polish, scratches, or small depressions is an example. Frictional resistance may be such a small proportion of the total draft that large changes in the microshape and, consequently, the coefficient of friction may cause only a very small change in total draft. On the other hand, microshape could affect other aspects of

FIGURE 157.—A, Curved subsoilers operated at design depth; B, curved sub- soUer operated deeper than design depth ; (7, curved subsoiler scaled in size to operate at increased depth. SOIL DYNAMICS IN TILLAGE AND TRACTION 233 soil movement such as scouring so that it is important even if draft is essentially unaffected. As a general rule, frictional resistance should always be minimized and control of microshape is the mest practical way to do this. , ^ i .i .i x i A As discussed in section 2.9.2, the properties of both the tool and the soil affect friction at the sliding interface. Unfortunately, only the properties of the tool may be altered since the properties ot soil usually cannot be controlled. Eare situations may occur where properties of the soil can be changed. For example, m a layered soil one horizon may offer lower friction than another and the tool can'be operated in that horizon. Shallow plowing to enhance scouring is common. Choosing the proper time for tillage so that the moisture content of the soil is suitable is another possibility tor "changing the properties of the soil." Generally, however, the tool must be altered to minimize frictional resistance. Efforts have not been made to incorporate soil-tool friction into empirically developed design equations. Examples in chapter 4 showed how friction can be handled in the derived approach, in the empirical design equations, soil-tool friction does not appear directly; rather, it appears indirectly through some expression o± microshape. Consequently, in all studies associated with soil-tool friction, shape has been kept constant and the coefficient of friction or microshape has been varied. In equations 132 and 133, microshape will have to appear as an integral part of Ts. Presumably, relationships can be quantitatively established by first relating the macroshape aspects of Ts to their respective dependent variables. At constant levels of macroshape descriptions, microshape can then be varied to establish the relations. Variation of soil frictional properties caused by soil conditions will be directly assessed by bi m equations 132 and 133.- Thus, although friction has not been qualitatively incorporated into design equations, there is no reason tor not doing so. . ^ P • x- i • 4. One of the most direct methods of reducing the frictional resistance of a tool is to improve the microshape—that is, to decrease surface roughness. Considerable effort has been made to achieve and maintain smooth sliding surfaces on tools. Initial polish required on a surface depends on whether scouring occurs. It scouring occurs, the abrasiveness of soil soon establishes an equilibrium surface roughness on the sliding surface of the tool. Depending on the soil and the initial polish of the tool, the polish of the equilibrium surface may be higher or lower than the initial condition. In some soils, however, self-polishing does not readily occur. In these soils, the polish of the surface must be established and maintained. Bacon ( 24 ) has reported that scouring may be poor m some soils if, after plowing, the tool is exposed to air drying tor a short time. Apparently the conditioning of the surface is lost through drying. The chemical and physical surface reactions that cause the difficulties have not been studied. In these soils, protect- ing films of oil or other preservatives are required when the tool is not in use. /v. • ^ ü V^- The inñuence of surface roughness on the coetticient ot sliding friction is indicated in table 17. While the magnitude of the rough- 2M AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE ness is not known, it is apparent that polishing a surface is a means of reducing soil-metal friction. Another aspect of microshape lies in the irregularities in a sur-

~~TABLE 17.—Effect of the surface condition of a tool on the coefficient of soil-metal friction in several soils'~~

Coefficient of soil-metal Sou friction for surface with— High polish Ordinary polish^ Sand — 0^ Sand (%) and Cecil clay (%)_ jai Cecil clav M 3A Siisaiic^hanna clav - .48 .59 T^iifkin clav .48 .51 1 Summarized from 1,000 measurements. 2 Surface normally i)r()vided by manufacturers of tillage tools. SOURCE : Nichols ( 3/6 ). face. Pits or other low spots, sharp changes in surface direction, or even shapes having different radii of curvature without a gradual transition may "trap" soil. The trapped soil forms soil bodies on localized areas of the surface (fig. 158). Generally, the low spots tend to protect the soil bodies so that tangential forces cannot move

FiouBE 158.—Soil bodies formed along the sliding surface of a tool because of minor surface Irregularities. SOIL DYNAMICS IN TILLAGE AND TRACTION 235 them along the surface. The effect on draft performance of these nonscouring spots depends on the area of the spots as compared to the total surface. Friction is greatly modified by adhesion. As discussed m section 2.9.3, adhesion results primarily from moisture films that increase the perpendicular attractive forces between soil and the sliding surface of a tool. Adhesion may be reduced by using a material that does not readily wet with water. Polytetrafluoroethylene and polyethylene, which have nonwetting characteristics, are currently being used as coatings on moldboard plows and other tools ( 81^ 336), The coefficient of friction of these materials can be as much as 50 percent less than that of smooth steel {93, 133), When lack of scouring is a problem, polytetrafluoroethylene can improve scouring so that the full draft may be reduced as much as 25 percent (table 18). Once applied to a sliding surface the material remains effective until it is worn away by the abrasive action of soil.

~~TABLE l'è,—Effect of folytetrafiuoToetliylene flow coverings^ on the draft force of plows operating at two speeds in clay soils~~

Draft force Plow surface Decatur clay Davidson clay 1 m.p.h. 3.5 m.p.h. 1 m.p.h. 3.5 m.p.h. Pounds Pounds Pounds Pounds Steel 450 490 480 575 Polytetrafluoroethylene- covered moldboard and steel share 390 485 420 530 Polytetrafluoroethylene- covered moldboard and share 365 430 310 440

~~SOURCE : Cooper and McCreery {81 ).~~

Lack of abrasive resistance is the biggest drawback to most nonwetting materials. Kummer and Nichols ( 235 ) and Bacon ( 23 ) studied the adhesion of soil with a number of materials such as wood, steel, and iron. Each material is limited by its wettability or its lack of resistance to abrasion. Some of the recentl}^ developed plastic materials appear to be the best materials available. For example, in a relatively abrasive soil a plow covering of polytetrafluoroethylene 0.2 inch thick appears to last for at least 50 acres and a plow covering of high-density polyethylene 0.2 inch thick lasts for at least 20 acres {81), In less abrasive soils, both materials last considerably longer. The requirements for a nonadhesive abrasion-resistant material are known, but no material available at this time (1965) is completely suitable. The high cost and short wearing life of available materials are the main limiting factors. The adhesion between soil and the tool has been reduced by heat. Experiments utilizing this approach have been reported by Bacon {23)^ but no practical method has been developed. Heat requirements have not been studied thoroughly, but in any study of heat requirements new energy sources would have to be considered in 236 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE order to determine whether the required heat could be economically produced. Nichols ( 312 ) has reported the only quantitative data concerning the influence of heat on adhesion. As shown in table 19, the coefficient of friction of a hot slider was considerably less than that of a wetted slider. Unfortunately, no details are available as to the temperature used or the quantity of heat lost from the slider during the operation. As an application, this method of reducing adhesion remains essentially untried.

~~TABLE 19.- -Effect of heat on adhesion^ as measured hy the coefficient of friction of steel sliders on dry sand~~

~~Slider Slider condition weight (grams) Dry Wet Hot~~

~~1,500 /^' 0.266 0.333 0.250 3,000 .266 .333 4,500 _ .250 .266 .333 .244 SOURCE: Nichols ( n2).~~

When the moisture content of soil is increased to the saturation point, the adhesion between soil and the tool may be eliminated. Adding water to the surface through small holes has increased the scouring qualities in clay soils {311), but the amount of water that IS required has not been accurately determined. Less water might be required than first appears likely, since only the sliding surface needs to be wetted. Indeed, the sliding surface may be saturated while the general soil mass is maintained at a low moisture content m which good pulverization is obtained. Within the range of field inoisture conditions, increases in soil moisture may increase the draft ot the tool even though the mechanical strength of the soil remains the same ( 376), Table 20 indicates the draft differences that can be attributed to increases in soil moisture. While one may choose to operate a plow m a saturated soil with the idea of reducing draft, the loss of traction and the possibility of dangerously compacting soil may preclude this approach as a solution to the adhesion problem. Bertelsen (.^0, 1^1 ) has proposed that an airblast be used to reduce the frictional resistance of a moldboard plow. Conceivably,

~~TABLE 2^,—Effect of the mmsture content of soil on the draft force of a moldboard plow in Houston clay soil~~

~~Moisture content! Pore Bulk Draft force (percent) saturation density of plow~~

Percent Qm./cc. 15.9_ Pounds 29.9 1.23 689 17.4_ 34.2 1.30 20.1_ 776 21.2 1.18 806 ercenf^^^^^^^^ percentage is 33.0 percent ; 15 atmosphere percentage is 22.5 SOIL DYNAMICS IN TILLAGE AND TRACTION 237 the action of the air could eliminate any friction between a tool and soil. Figure 159 shows a scheme for introducing a cushion of air between the soil and the tool surface. The effectiveness of this scheme is influenced by the permeability of soil to airflow, since.a

~~SOURCE OF COMPRESSED AIR~~

~~FIGURE 159.—Reducing sliding friction with an air cushion.~~

resistance to airflow is required in order to build up pressure and, hence, the air cushion. With a film of air between the soil surface and the tool, the coefficient of friction should be greatly reduced. Bigsby ( 42 ) was unable to reduce the draft of model tools with airflows up to 70 cubic feet per square foot per minute at a pressure of 1.0 pound per square inch. He passed air through various configurations and sizes of holes. In one arrangement, holes 0.028 inch in diameter drilled approximately 0.07 inch apart trapped grains of soil and made a rougher surface so that the draft was increased rather than decreased. Measurements reflecting the impedance to airflow were not reported, nor were they correlated with the draft data. Until further studies have been made, the use of an air cushion to reduce friction must be classed as an idea rather than a useful development. Providing either a moving or a smaller surface, or a combination of both, is another means of reducing friction. Skromme {S90)^ Kummer {231t,), Getzlaff ( lU, H5 ), Dufour, as reported by Getz- laff \lU), Gantt {137), and Gordon ( 159 ) are among those who have substituted belts, rollers, and rotating disks and colters for a stationary sliding surface. In these approaches, the moving parts in contact with the soil actually transport the soil so that little sliding occurs. Moving parts in contact with soil are undesirable because of mechanical requirements, but this limitation should not preclude utilization of the principle. The slatted moldboard plow is an example of a tool that provides a smaller surface. By decreasing the area of contact between the tool and the soil, adhesion is decreased. At the same time, the tangential forces available to move the soil along the surface are increased. Both effects are directly proportional to the ratio of the 238 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE area of slats to the area of open space between the slats. Japanese manufacturers reportedly have found that in certain instances ^f?^ .^ -^^^^^ ^'""^ ''^t*®^ ^®s"^ts than fixed slats. Success of the slatted plow IS greatly influenced by the speed of operation. Figure 152 shows how the path of soil changes with speed. Unless the path of movement parallels the direction of the slats, the benefits of reduced area will probably be lost. Most of the techniques and procedures tor reducmg friction have practical value only when there is slîdfr^fricfioï' ^^^"^ *^^ *'*^''^ '^'"''** '^ appreciably affected by The soil-niampulating characteristics of a tool are specified by the terms i, and i „in the soil manipulation equation 133. The terms are, in turn defined by macroshape descriptions, but nothing in either the relation or the description indicates why the various shapes were selected. Most shapes have been developed by inven- tion. Ihe tillage action required to create a desired soil condition IS envisioned and then developed by trial and error. In drawn tools, in which the path of movement T^ is a straight line, design emphasi^ is almost exclusively placed on the influence of the shale íd^ttme^^y^tMs^elhoS:""' '"^^ ''°''" ™^^ "^ qualitatively The amount of strain induced into the soil by the movement of a tool ot any shape determines in part the amount of shear and movement in the soil reaction. The depth of operation and the lift of the r^ÍT^ adjusted to obtain the desired effect. Unfortunately, most tillage tools have a fixed ratio in these respects so that the optimum soil reaction may not always be obtained. Chase ( 67 ) and othere have studied lift angles in the design of subsurface tiller blades. Iwo distinct actions have been observed (fig. 160). The

~~'^'^^.^~~

~~^¡mmW'~~

FiGTJKE leO.-Effect of height of lift on the soil surface produced by a subsurface tillage blade. (Chase, Agr. Engin. (07).) low approach angle (16°), which accented soil cutting, controlled weeds much better tlian the higher approach angle, which accented the lifting action. By keeping the lift angle at approximately 16°, the surface of the soil was essentially level at the termination of SOIL DYNAMICS IN TILLAGE AND TRACTION 239 the operation. Since the tool was designed to cut weed roots, shatter of the soil and soil movement were not particularly desirable. A simple straight tool operating at right angles to the direction o± travel is seldom used. The blades are usually swept back at angles of 20° to 50°. This permits self-cleaning of the blade. Any alteration of the orientation of a sweptback tool with respect to a horizontal plane has a secondary effect on the depth of cutting (fig. 161). An increase in the approach angle of the tool shank ot

~~2:^~~

FIGURE 161.—Effect of tüting a sweptback blade on depth of tiUage. (Chase, Agr. Engin. ( 67 ).) a drawn tool essentially constitutes a means of changing tool shape. In a number of applications, the elevation of the outer ends ot the blade may be undesirable because the cut cannot be kept at a uniform depth. The depth of cutting is frequently dictated by the location of plant roots ( 17S ) and only by prior excavation of the soil can the desired depth be determined. The upheaval of soil around a deeply operated tillage tool generally is similar to that of soil reacting around a tool having a large depth-to-width ratio. As shown in figure 96, there is a point below which the soil does not move upward. Below this point the soil moves laterally so that it passes around the sides of the tool without any upward movement, and the resulting soil condition is a deep vertical slot. These slots are frequently so narrow that they may be bridged over when a load is applied to the surface {321), Be- cause of this bridging, the lower part of the channel may remain open, as shown in figure 162. This characteristic bridging of the soil has been utilized in the design and operation of mole dram plows. These plows penetrate the soil to some depth and open a small drainage channel. The design of the mole has been achieved by trial and error; it is not based upon any theoretical considerations. According to Schwab, in the American Society of Agro- nomy's monograph on drainage ( ^ ), the size of moles varies con- 240 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

FIGURE 162.—Channels formed by a narrow tool operated in a wet clay soil. (Nichols and Reaves, Agr. Engin. ( 32Í ).) siderably. Most of the emphasis in mole drainage has been on controlling grade level, since the drains may become ineffective if the grade level is misât isfactory. A number of attempts have been made to increase the volume of soil that is shattered during deep tillage operations. Shattering is satisfactory only when the soil is dry and brittle. Under these conditions, the tool may create a general shear throughout the soil mass; but if the soil is hard aiul tough, the action of the tool may create large clods that are very difficult to handle in any subsequent tillage operation. The addition of wings to a deep tillage tool increases the volume of soil that is lifted and shattered. As a residt, a larger volume of soil is broken up (fig. 163). These wings or lateral blades have normally been attached near the bottom of the tool. Several forms of these tools have been studied, but much infornuition is still lacking.

FiouBE 163.- -Soil volume disturbed by : A, A simple chisel ; B, a cliisel with wings. SOIL DYNAMICS IN TILLAGE AND TRACTION 211 The importance of the length and lift angle of the point of deep tillage tools has not been fully determined. These factors contribute to the vertical forces that hold the tool at the desired depth ni the soil without additional weight and still provide an optimum draft force. Preliminary results indicate that point angles in excess of 35° should be studied. Small differences in the width of points on narrow chisels have little influence on the draft of the tool when it is in a soil where shatter takes place. The major consumption of energy is the shear of the soil rather than the subsequent displacement required for passage of the tool. In addition to wings, novel designs utilizing large attachments have been developed to increase shatter of the soil. One of these designs used a spinner that was free to rotate and grind the soil into a finer condition (fig. 164). No real evidence of this action has

~~— ^~~

~~FIGURE 164.—Deep tillage tool with a freely rotating spinner intended to cause greater pulverization of the soil.~~

been found, and the spinner increased the draft of the tool approximately 8 percent. No attempt has been made to introduce power into the soil by driving the spinner during operation; possibly this would have a pronounced granulating effect. There are instances when intuition indicates that a particular movement of soil might be accomplished more readily by the inde- Eendent action of several shapes than by a single shape. Soil may e inverted by a moldboard plow, but some mixing within the furrow slice usually occurs. Where a thin surface layer is to be completely covered, it might be expedient to use two decisive actions. The first cuts the layer loose and deposits it in the bottom of the furrow- while the second covers the deposit without mixing. This might be desired when radioactive dust or some other material must be buried. Figure 165 shows the actions accomplished by plowing a deep furrow and using a small skimmer blade or plow to push the surface material into the bottom of the previously created furrow. Depending 242 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~FIGURE 165.—Simple soil-covering motions.~~

on the size of cut, depth of placement may be accurately controlled. When large areas are to be decontaminated or when radioactive material IS withm a zone where it could be retrieved by plant roots, complete excavation and removal of the material may be necessary ( 297 ). An example of cultivation where inversion is not desired IS the Mal'tsev system of cultivation in the U.S.S.E. {W). An- other example is dryland farming in the semiarid Western United btates where a moldboardless plow induces a shearing action throughout the soil, but the action does not result in inversion of the soil. This type of tool design does not expose moist soil to the atmosphere and the design has a useful purpose—to conserve moisture. Thus, üie shape of tools as represented by T, may be guided by intuition, ihe extent to which these shapes represent ideal or optimum shapes can be determined only after establishing shape-performance relations. 5.3.7.3 Edgeshape and Wear As defined in section 5.3.1.1, edgeshape refers to the shape of edges of the finite tool surface that comes in contact with the soil. Usually the overall tool shape has no relation to its edgeshape. For example, figure 166 shows how the basic form of several spherical disks is

~~REVERSE SPHERICAL CONE NOTCHED WAVY CURVATURE~~

FIGURE 166.—Disk tool shapes. modified by notched and wavy edges. Thus, the same macroshape of the tool may be modified by different edgeshapes. On the other hand, the macroshapes of reversed curvature, spherical, and cone disks are basically diiferent but the disks could have the same edgeshapes. Figure 167 shows how sharpening disk edges can produce diflerent edgeshapes. In spite of the small area of the edge as compared to the total area o± the tool, the shape of the edge can affect the total draft of the SOIL DYNAMICS IN TILLAGE AND TRACTION 243

~~(A) (B)~~

~~(C) (D)~~

~~(E) (F)~~

~~FIGURE 167.—Edgeshapes commonly used on disks. (McCreery, Amer. Soc. Agr. Engin. {262).)~~

~~INSIDE BEVEL 400 OUTSIDE BEVEL (A)~~

~~200~~

~~OLHI-~~

~~(B) Ö -2001- £ _J -400 • L-Hh~~

~~-200~~

~~-400 L. "20^ 30 DISK ANGLE i")~~

tional Tillage Machinery Laboratory {311 ).) 244 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE disk (262). Figure 168 shows the effect of sharpening on the forces of a disk. Chase ( 67 ) reported that the angle of the approach edge is important. Figure 169 shows how an upper and a lower bevel on the edge of a plane tool affected soil movement. When the bevel was on the upper surface, a "low pressure area" caused the soil to adhere to the surface as shown at the right in rigure 169. Soil adherence in-

FIGURE 169.—The influence of edgeshape on soil movement over a tool. (Chase, Agr. Engin. ( 67 ).) creased the draft of the tool. When the bevel was on the lower side of the surface, sticking was not observed. Chase also reported that tools needed sharpening more frequently when the bevel was on the top. The forward edge of a tool, such as the share of a moldboard plow, can cause soil compaction if it becomes blunt. Figure 170 shows how compaction is caused through the movement of the soil. The blunt edge shown simulates a dull share except that the edge is approximately 10 times thicker than that of a normal share. Thus, the effect was exaggerated so that movement of soil particles along a glass plate coated with powdered aluminum could be photographed to indicate the effect. The blunt edge Ä caused a buildup of soil, which in turn forced some soil to move downward and cause compaction at G. Soil in areas B and C moved upward into a zone of less confinement. Vertical cracks in the bottom of a furrow of a moldboard plow, similar to those seen at area H, have also been observed with earth-moving equipment {338). Forces resulting from a blunt edge applied to the soil in the direction of travel cause the soil to pull apart. The number and size of the cracks depend on soil conditions. The compacted zone may be very thin and consequently of little significance. In wet soils, however, the smearing action could conceivably close the soil pores completely so that no air or water could be transferred across the layer. A practical example of the detrimental effect of compaction was reported by workers at the Eoad Research Laboratory {370). They found that in making small cuts with a rotary tiller the cutting blade had to pass through an area SOIL DYNAMICS IN TILLAGE AND TRACTION 245

FIGURE 170.—The compaction of soil by a blunt-edged tool. (Nichols, Reed, and Reaves, Agr. Engin. ( 32i ).) compacted by the previous blade. Figure 171, A shows how a zone compacted by a i)i'evioiis cut of a dull blade (shaded area) can lie brought into the zone of cutting of a subsequent blade when a small cut is used. A greater cutting force is required if a dull blade causes compaction and subseijuently is operated in the compacted zone. Measurements of power required as compared witli size of cut confirmed tliose observations. Soil compaction caused by a dull blade usually occurs because wear has modified the edge shape. The edges of a tool surface are usually the first element of the tool to encounter the .soil and as a result they are subjected to greater forces and wear. Furthermore,

~~M^//¿^//~~

~~(A) (B)~~

FIGURE 171.—Location of soil compacted by a dull rotary cutter, and area of cut: A, Small cuts; B, large cuts. 246 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE because of their small area and the concentration of wear, edges tend to change their shape rapidly. The macroshape of the entire tool generally remains relatively unchanged as wear progresses. Edge- shape, on the other hand, is greatly changed with wear so that wear and edgeshape must be considered simultaneously, ^i."^^^ radical change in edgeshape that can occur in plowshares and the change m forces required to operate the plow bottom are shown m table 21. Change m edgeshape due to wear can produce a significant eflect on forces on both rolling and rigid tools (fig. 162). A

~~TABLE 21.-—Effect of worn shares on the forces on a plow~~

~~Measured forces on plow Type of share Draft Vertical Side Pounds Pounds Pounds New- 317 25 73~~

~~Worn_ 333 -92 49~~

~~New__ 266 51 66~~

~~Worn_ 333 -74 57~~

~~New. 290 33 64~~

~~Worn_ 435 <^ -164 60~~

SOURCE : Nichols, Reed, and Reaves, Agr. Engin. { S2Ji. ). negative vertical force, as shown in table 21, indicates that the bottom had to be held m the soil to operate at the designated depth A positive vertical force indicates that the plow had to be held upward to prevent it from going deeper. In normal operations the moldboard plow IS free to float and seek its natural depth as a result of the balance of forces. Gavrilov and Kofuschkin ( 1^0 ) determined the coeliicient of depth variation for new and worn plowshares. They deñned the width of chamfer as the length of the line A and C shown Í? uPin -^1^^' ^1^^^ ^^®^ ^^^ increasing width as a criterion of wear, iable 22 shows how the coefficient of variation increased as the width o± chamfer increased and the average furrow depth decreased beveral researchers have demonstrated that wear occurs rapidly Cjayrilov and Koruschkin {UO) showed that wear increased draft resistance as much as 30 percent (table 23), and that nearly half of the increase had occurred after only a few acres of land had been SOIL DYNAMICS IN TILLAGE AND TRACTION 247

~~TABLE 22.—Effect of the width of chamfer on the average depth of furrow in a sandy loam soil~~

Coefficient of Width of Average depth chamfer variation in of furrow (millimeters) furrow depth Centimeters Percent 0 21 8.7 9 _ - 20 9.9 12 20 11.4 15 18 16.0 SOURCE : Gavrilov and Koruschkin mO ). plowed. Figure 172 shows how the specific resistance of new and worn shares increased with hours of operation. The rapid increase in total draft detected after a few hours of operating time indicates significance of wear.

~~^ 0.56~~

~~g 0.54 WORN-^ u, 0.52 o § 0.50 CO 520~~

~~UJ a: o 18 WORN- 0.46 t NEW g 044~~

~~£8 '^ -I I L—J ^ 0.42 ' ' I » 18 20 22 24 26 28 30 18 20 22 24 26 28 30 TIME (hr) TIME (hr)~~

~~FIGURE 172.—Effect of wear on specific plow resistance and fuel consumption. (Karatish {206).)~~

Karatish ( 206 ) studied the rate of wear from a different perspective. In irrigated areas the resistance of the soil can be altered by changes in soil-moisture content. He found that the life of plowshares varied with soil-moisture content. For a sandy loam soil, the share life increased from 4 acres at a moisture content of 6 to 7 percent to 6 acres at 12 to 13 percent ; and further to 16 acres at 16 to 18 percent. . . Any factor that increases the normal force along the sliding surface increases friction and wear. On tillage tools, leading edges are generally subject to the highest wear rates. The effect of normal force explains the rapid wear of tools or portions of tools that follow load-bearing wheels. These load-bearing wheels compact the soil and increase soil strength so that the force required to displace the soil increases and, hence, the normal force on the edges increases. Figure 173 shows the accelerated wear that occurred on the portion 248 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE TABLE 22,.—Effect of wear on the angle of sharpness and specific draft resistance of plows

Soil type Angle of Specific Increase in and sharpness of draft draft area plowed plow share resistance resistance (acres) Degrees Kg./em'. Percent Loam : 0 15 0.50 0 4.9 30 ..59 18 12.0 36 .63 26 17.0 42 .66 32 Sand : 0 _ - - 15 .31 0 6 . 28 .35 13 14 . 32 .37 19 30 40 .40 29 SOURCE: Gavrilov and Koriischkin ( ///O ).

of a blade operating behind a wheel. The area to the extreme left of the figure shows accelerated wear due to a wheel track. Gangs of disks also illustrate the increased normal force that causes increased wear. The end disks are subjected to larger soil forces because of their physical location in a gang of disks. The larger forces on end

~~'^ké^Ê^ ^~~

FIGURE 173.—Accelerated wear of flat blade by compacted wheel track. (Photograph courtesy of Kansas State University.) SOIL DYNAMICS IN TILLAGE AND TRACTION 249 disks are caused by the soil they must move because of their position and because they tend to operate deeper than the center disks of a gang. Data from field experiments (table 24) indicate that end disks wear nearly three times faster than center disks {353), Position, therefore, affects normal force and thus affects wear and changes m tool shape.

~~TABLE 2^,—Weight loss of disks operating at different positions in a disk gang~~

~~Weight loss per Disk position 100 hours of use Pounds End disk- 1.58 2d disk- .96 ed disk- .83 4th disk- .57~~

Wear is a complicated process that involves not only the properties of the tool material but also those of soil {8, 59, 336, 360, 368), Furthermore, available data indicate that the rate of wear is ]ust as important as the amount of wear. Little has been done to study wear except to use wear-resistant materials. So-called hard surface materials are often expensive; consequently, they are applied only to leading edges of tools and other areas that wear rapidly. Much more research is required to unravel the wearing process. Quantitative relations that result in wear behavior equations ultimately will have to be developed. Empirically, wear can perhaps be quantitatively described in terms of altered shape. Since wear appears to change edgeshape so rapidly, perhaps only worn edgeshapes should be used as variables of macroshape m design equations. Efforts have not been made to include edgeshape or wear into tiie design equations; however, for design to be complete, these special shape factors must be included. Edgeshape must first be described qualitatively and then quantitatively, and the description must be related to its functionally dependent factors. Probably a more realistic approach would represent edgeshape and wear as modifiers o± the macroshape design equations in a manner similar to that done tor friction in section 5.3.1.2. 5.3.2 Soil Transporting Tools All soil manipulating tools apply dominant forces that produce compacting, loosening, or turning of soil, or some combination ot these. In many instances the purpose of soil manipulation is simply to transport soil from one location to another and any loosening or turning that occurs is incidental. Land leveling and road building are two obvious examples where movement may be more important than soil breakup. Soil transporting tools comprise a second large category of soil manipulating tools because their purpose is different from that of soil loosening or turning tools. Soil is transported by two basic methods. For short distances, soil is literally pushed or rolled over itself in a process often called bull- 250 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE dozing. For longer distances, soil is usually loaded into self-loading Sf%h *^'* '' T ^ ^'^''^^''^ carriedâther than pushed ovef itselt Ihe macroshape, microshape, and edgeshape of tool surfaces tooT te?.-*'"^ ""'^ ^''^'i^ ^"^"«^ «™" performance of tL ;^. V, J?î^ des gn purposes, shape should be quantitatively related to he functionally dependent variables indicated in equations 132 and Sfiii -"i ' ''^ '""'^ manipulation in transporting tools can be relativelj^ easily expressed when the volume or mass of soil moved IS the primary factor of importance. Thus, all that has been slid concerning the empirical development of des gn equations appUes to vto^d^Trâ.^ f^\ Only limited efforts Íave\een ¿adTto dí yelop design equations for soil transporting tools, but available auali- tatîve mformation may be used to Sevelof basic' trends aperCm-

T.iiíi""^'!^'"^■' ^ ?'"^'''^^ ^^^^^.'^ "^«^^*i th^o'igh soil to loosen and Ar ""^^^^'^ transport soil over short distances. For most effective performance, the blade should be filled to its maximum capacity and require the least force to be moved. Moving sou bv rollmg requires less force than moving it by sliding. sLe sous such as sods or plast c soils can be rollfd up In front^of a Sade in causL Sy s"llin,f i^^^^ble flow of soilln front of a blade thlí causes rolling is illustrated on the right in figure 174. Unless a roll

~~"iSAÏl*" --.Î'??..-ASä.'^^'^S-Ä~~

IV^^f^' rolling is not efficient; a flattened roll tends to slide and KÍ rÄlf T "^""fr' rr^ periodically as the roll flops over Kuhn ( mß, m ) and Garbotz and Drees ( 138 ) studied the effect of the shapes of blades on their ease of filling and their draft requiS W .n ^^'' Parabolic blade (fig. 174) permitted a collapse of IS so ttiat some pushing rather than rolling was necessary. The two in volutes resulted m good rolling. The force required to operate thê Th« rLTu "V^^s^red m two soil types at one speed and one deX Se TtabfetT '41.."^^°^'?^/? '\^ ^"^^^ «^ inclination of^the do i^îSfilV ,^lthough the data show no consistent trend, they do indicate that shape can be extremely important. In the sandv silt soil, the angle of inclination changed draft by a factor of two foî volutetoUe AtI and thew otherrÎ^^Î^:, two blades ^Y also ^^^«^^^«âccounted i^for «hape a change between in draft in- of a factor of two In other data not reported here, a mofe ncHned Sn.f^ a smaller draft at varying speeds and depths. No consistent trend was apparent between depth and blade shape. The SOIL DYNAMICS IN TILLAGE AND TRACTION 251

~~F^RABOLA INVOLUTE I INVOLUTE 31~~

~~FIGURE 175.—Detailed shapes of blades shown in figure 174. (Garbotz and Drees, Westdeutcher Verlag GMBH {138).)~~

~~possibilities of improved design through the development of equations 132 and 133 should stimulate a continuation of this type ot~~

Characteristic shapes of blades that have been developed for bulldozing (fig. 176) have been identified in terms of their mfluence on performance. An increase in filling resistance caused by an undesirable flow of soil may result from adhesion of soil at some low place along the blade. A recess behind the cutting edge (ñg. 176, A ) creates a pocket in which soil adheres; this soil can mcrease frictional resistance along the surface of the blade. Soil may also stick when the radii of curvature between two adjacent sections o± blade ditter

~~TABLE 26.—Draft force as affected ly the angle of inclination of a leveling Uade operated at a depth of k centimeters and at a speed of 2 hilometers per hour~~

Sou type Draft force for a blade and angle of2 3_ shape of tooli -15° -8° 0° +10*» Kg./mß Kg./mß Kg./m.^ Kg./m.^ Medium sand: Parabola 2,500 2,850 3,430 Involute I 2,830 2,800 3,500 Involute II 2,620 2,540 3,640 Sandy silt: — Parabola - 5,500 7,000 10,400 Involute I 3,150 3,350 4,150 Involute II 6,780 8,100 11,200 - 1 Blades were 100 cm. long and 450 cm. high. Shapes are shown in figure 175. 2 Blade angle was measured between a Une drawn between the upper ana lower edges of the blade and the vertical. When tUted back the angle was nesrative j 3 Draft force measurements are based on the volume of soU on the blade. SOURCE : Garbotz and Drees, Westdeutscher Verlag GMBH {138). 252 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~FIGURE 176.—Soil reactions as influenced by blade shape. (Kuhn, Ztschr Ver. Dtsch. Inge. ( 233 ).~~

by a factor of more than 1.5 (fig. 176, B and O). In sticky soils, an accumula,tion of soil at the top of the blade (fig. 176, Z?) may ¿re- vent the blade from filling. If the top of the blade is tilted Kar forward, (fig. 176, F) soil will again adhere. A good shape, similar to that m figure 176, E, will fill completely and permit good soil movement. A good or practical shape is really a compromise of fnTfi "lî^liêd shapes that serve special purposes. When used as an isolated specific blade for one type of soil manipulation, the number of specialized shape characteristics may be limited, and an actual desim may overemphasize one particular characteristic. Jîgure 177 indicates several idealized shape characteristics associated with specific soil handling functions. An integration of appropriate features from the idealized shapes provides a start for designing a blade for some particular purpose. When soil must be transported over distances that make bulldozing W.T™'''^ •' "r""^?,^""u. ""î"^ "'^^- L^y«^« «Í soil are generally cut ôse by an mclmed blade and the separated soil is collected in a wheeled device for transportation. Figure 178 shows a general ar- X?îrV*/ '^**-"^ ^1^1*^^' '^°^^ *^ ^«"««t soil' and^ transport Wl t J. • A «1^^? problems in designing a scraper so that a full aï(2) fh^shipe'Ä bo^wl.^'^ *'^ '^''^ ^' '^^ «"^*-^ ''^'^ Garbotz and Drees ( 138 ) studied the influence of angle of inclina- üon and depth of cut on the draft force of large indined blades The blades were 1,000 millimeters wide and were 450, 308, and 218 millimeters long, respectively, for blade angles of 20°, 30°, and 45° Eesults show that an angle of approximately 30° is opt mum foi^ minimum draft (fig. 179). The minimum draft coincideT^^th a SOIL DYNAMICS IN TILLAGE AND TRACTION 253

~~PENETRATING CUTTING PILING HOLDING~~

~~EMPTYING LEVELLING CARRYING ROLLING~~

~~FIGURE 177.—Idealized functional shapes for bulldozer blades. (Kuhn, Ztschr. Ver. Dtsch. Inge. (232).)~~

FIGURE 178.—Paths of succeeding loading increments in a large scraper. depth-of-cut to height-of-lift ratio of 1:3 and a depth-of-cut to length-of-knife ratio of 1: 9. While these data provide definite design information, any recommendations should be considered only as first approximations of the information required for complete design. . . . , Perhaps the most difficult problem m designmg a scraper is to insure filling the bowl. When a large volume of soil must be moved by sliding, the weight of the soil itself adds to the normal load and hence increases the tangential force required to slide the soil. In a scraper, the weight can become so great that the force required to push soil into the bowl may confine the movement of any new soil that attempts to enter the bowl. In such instances, soil is bulldozed in 254 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~o 6000~~

~~3 ^4000 100 mm p~~

~~Ö z 2000 I 20* 30*» 45*» BLADE ANGLE (•)~~

~~FIGURE 179.—Effect of depth of cut and angle of inclination on the draft of an inclined blade. (Garbotz and Drees, Westdeutscher Verlag GMBH ( 138 ).)~~

front of the cutting blade with no further filling {338), Increasing the depth of cut may supply somewhat greater force to move the accumulating soil. But confining resistance will again be reached and bulldozing will start when the forces involved come into equilibrium. While still deeper cuts will continue to provide more shov- mg force for filling, more force must be applied to the scraper so that traction or engine stall soon becomes a limiting factor. Shape of the bowl, so as to obtain a smooth flow of soil while the bowl fills, thus becomes an important design consideration. One of the first possibilities of shape design is to have the bowl conform to the reaction of the soil. For example, areas designated A and B in figure 178 usually will not fill ; therefore, their size may be decreased if the saving in material and weight is significant. A short distance from the cutting blade to the back of the bowl to decrease the distance that soil must be pushed seems imperative. A shallow bowl to minimize the height of soil buildup also is desirable. Since practical limitations on width are self-evident, short lengths and shallow depths restrict the volume of soil that a bowl can hold. Consequently, size, shape, and orientation influence the filling resistance of a bowl. Unfortunately, these factors have not been studied sufficiently to indicate optimum values. Use of an inverted elevator is a positive means of obtaining better filling. The elevator minimizes the need to force soil through and over soil in order to fill the bowl of a scraper (fig. 180). By minimizing the need to push soil into the bowl, forces on the cutting blade are also reduced. This reduction decreases the cutting force required to operate the cutting blade, and the total draft of a scraper is greatly reduced. The manufacturer of a scraper employing an inverted elevator reports that the total power required is divided equally between the elevator and the drawbar. SOIL DYNAMICS IN TILLAGE AND TRACTION 255

~~FIGURE 180.—An inverted elevator to assist in filling scrapers.~~

5.3.3 Conclusions Macrosurface and edgeshape are important in the design of soil loosening and turning tools and soil transporting tools. Consider- able effort has been made to obtain design information; however, much remains to be done in terms of developing design equations. Only Ashby (equation 141) has tried to develop a design equation that will permit quantitative designs to be effected, and this he did in 1931. All other studies have related shape to design only in a qualitative way. Admittedly, qualitative information is needed. On the other hand, striving to develop design equations can provide the same information and also lead to the equations. The goals are clear and the path is direct so that only the work remains to be done. 5.4 Manner of Movement Once the shape of a soil manipulating tool has been selected, only the manner in which the tool is moved through soil can be altered to effect different manipulations. Manner of movement involves orientation of the tool (angle of approach), its path through soil (depth of cut), and its speed along the path. Shape of a tool is usually determined when the tool is manufactured. Once fabricated, the shape is usually not easily altered, so that the manner of movement is generally changed during actual use in order to effect the best performance ( 122 ). Shape is primarily controlled by the designer, who is associated with the manufacturer. Manner of movement, on the other hand, is primarily controlled by the user. But each tool has inherent limitations in its practical method of operation that limit variation in manner of movement. The problems encountered when considering the manner of movement in design are essentially the same as those encountered when considering shape. First, the manner of movement must be described ; second, the description must be quantitatively related to the dependent functional factors—forces and results of soil manipulation. Just as shape is meaningless without specifying manner of movement, so manner of movement is meaningless without specifying shape. Neither can be considered to the exclusion of the other. In- deed, this is the crux of the design problem. Each abstract design factor influences the operational performance of the tool. Only 256 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE from quantitative data on all factors to be considered is it possible to develop an optimum design for some intended soil manipulation. In order to develop the required information, each factor must be isolated and studied independently so that its effect can be quantitatively assessed and related to resultant forces and soil manipulation, as implied by equations 132 and 133. After quantitative information is available, it can presumably be mathematically combined to permit true design. Until such information is available, however, a researcher needs to simplify the system of interest in order to gain an understanding of it. The factors involved in both shape and manner of movement must be isolated and investigated in order to accomplish this simplification. 5.4.1 Orientation Orientation must be specified before it can be incorporated into design. Mathematically, the specification is usually simple. Orien- tation relates the shape of a tool to its direction of travel. Since shape must be quantitatively described with respect to some coordinate system, orientation can be described by specifying the shape coordinate reference system with respect to the direction of travel. For example, as long as a plane tool is operated horizontally the orientation of its inclined plane is given by one angle—the angle between its surface and the direction of travel. Even with complex-shaped tools, shape reference axes can be orientated by specifying only two

Other convenient means may also be used to specify shape orientation. For simple shapes, angles that refer to a mounting device, a straight side or the bottom of the tool, or any other convenient plane or line can be used. For a curved surface, the orientation may be described with respect to a diameter, a line of symmetry, or an axis of rotation. Figure 181 illustrates some angles that may be used to specify orientation. Although angles such as these are convenient for many purposes, orientation of a shape reference system will prob-

~~CLEARANCE ANGLE (SPECIFY PLANE) LIFT ANGLE /APPROACH ANGLE\ \ VERTICAL PLANE/ DIRECTION OF TRAVEL SIDE ANGLE APPROACH ANGLE \ ^HORIZONTAL PLANE/.) TILT ANGLE SLANT ANGLE \ RPENDICULAR PLANE/~~

FIGURE 181.—Convenient orientation angles for tillage tools. SOIL DYNAMICS IN TILLAGE AND TRACTION 257 ably offer the simplest means of incorporating orientation into design equations, ni j Orientation of shape has many obvious effects. Move a moldboarcL plow sideways or to the rear, and orientation will completely defeat its intended purpose. Orientation also has some less obvious effects that influence performance of a tool. For example, McCreery and Nichols ( 263 ) found that orientation affected the rotation of a free-rolling spherical disk (fig. 182). Minimum rotation occurred

~~10 15 20 25 30 35 40 45 50 ANGLE OF TRAVEL (•)~~

FIGURE 182.—Effect of orientation on the free rotation of a disk. (McCreery and Nichols, Agr. Engin. {262).) when the vertical disk was operated at an approximate angle of 20 to the direction of travel. The significance of the rotation has not been explored so that the meaning or even the desirability of minimum rotation is not known. Since rotation obviously affects the amount of sliding between the disk and soil, friction and wear must be affected by the rotation. • ^' ^ ^ The approach angle (lift angle in fig. 181) of an inclined plane greatly affects both the normal pressure on the tool and the amount of soil disturbed by the tool. Figure 183 shows the average normal pressure on the sliding surface of a straight chisel operated 6 inches deep for all angles of inclination. A 90°-angle of inclination represents the tool operated in a vertical position. The decrease m average normal pressure with decreasing angle is also associated with reduced total draft. The reduced draft cannot be attributed entirely to the reduced frictional force involved in sliding soil across the chisel. Payne and Tanner ( 332 ) showed how the approach angle of a straight chisel affects the shape and volume of soil disturbed (fig. 184). They did not report on the amount of soil breakup (average clod size). If soil breakup is the intended purpose of the manipulation, the volume disturbed does not necessarily reflect the breakup. Payne ( 332 ) reported that the draft of a straight chisel 4 inches 258 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~CO Û- SANDY LOAM ^ 40~~

~~CO CO UJ Of 30 < i 20H O 2 SAND CLAY UJ 10~~

LÜ

~~20 40 60 80 100 120 140 INCLINATION OF TOOL (<»)~~

~~FIGURE 183.—Average normal pressure on a straight chisel as affected by the approach angle. (Computed from Tanner, Jour. Agr. Engin. Res. (419).)~~

~~FIGURE 184 —Shape and volume of soil disturbed by a straight chisel as i? f?oo ^ *^^ approach angle. (Payne and Tanner, Jour. Agr. Engin. xCes. ( odd ). )~~

wide ranged^from 425 pounds at an approach angle of 160° to 90 pounds at 20°. These were mean values for several agricultural soils and indicate the effect of approach angle on draft. Orientation of a straight chisel thus can have varied effects. Orientation is sometimes used to control depth of tools, particularly moldboard plows, through the concept of "suction." A tool that has good suction is considered to penetrate well—it is sucked into the soil. Eesearchers in the past ( 27, 392 ) have defined suction in terms o± clearance angle (fig. 181). The clearance angle can be correlated with penetrating characteristics because of the inherent fixed relation between the lift angle and the clearance angle for any tool. In reality, however, penetration is determined by the magnitude and direction of the vertical forces acting on the tool. Within limits, these forces can be altered by increasing the lift angle or clearance angle tor a specific tool in order to increase suction. Hence, orienta- SOIL DYNAMICS IN TILLAGE AND TRACTION 259 tion, which determines the lift angle, can be used to increase or decrease suction. This principle was used to control depth of walking plows. By altering the hitch point, the orientation of the plow was changed so that the downward force of suction and the upward component of the line of pull came into equilibrium, and the plow "floated" at the depth that produced equilibrium. Even m some mounted plows today, the principle is used. .-..-, .. m Tanquary and Clyde {m) designed a special hydraulically actuated plow hitch that increases the approach angle of a tool as the tool enters the surface of the soil. The approach angle decreases as the plow penetrates soil and thereby decreases suction while the vertical component of the line of pull simultaneously increases. When the forces reach equilibrium, the plow floats and maintains the equilibrium depth. ^ .T, • Often the linkage system used to position a tool aflects both orientation and depth. Three commonly used linkages are radial, trapezoidal, and parallelogram. In a parallelogram linkage, orientation is essentially independent of depth, whereas in a radial linkage orientation changes as depth is changed. The trapezoidal Imkage system has intermediate characteristics. When penetration is difti- cult, a linkage system that does not permit a tool to quickly seek its operating depth may leave large areas at edges of fields that are tilled too shallow. Sineokov ( 388 ) calculated roughly the length ot path required for radial and parallelogram linkage hitch systems to reach operating depth. While studying simple chisels and sweeps, he secured fair agreement between the theoretical and experimentally determined path lengths obtained for the trapezoidal linkage system. The path required for a 27-centimeter sweep to reach operating depth decreased significantly as the suction increased. Sineokov suggested the following equation to express penetration relations observed for the sweep : S = acot(^), (142)

~~where S = distance required to reach depth, a — final equilibrium depth, €o = initial clearance at the time of entry into soil, € = clearance angle during operation.~~

Narrow chisels did not appear to be affected as much as the sweep was. Additional studies will be required before the distance of travel to reach operating depth can be determined in a rigorous manner. Another aspect of depth control-orientation interaction is shown in figure 185, where a radial linkage system is applied to a spring tpoth harrow. Not only is the angle of approach a changed with depth, but the volume of disturbed soil is also changed (fig. 184). Consequently, the distance between harrow teeth probably should be changed as depth is changed in order to manipulate the soil most effectively. Obviously, compromises must be made in these situations, or else entirely new principles of positioning will be needed for linkage systems. The possible interactions of orientation and depth or position control contribute to the difficulty and complexity 260 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~M^///j^///^/ \////^///A^j//^/ I M^m^///^Am~~

a = 0* a = 45** a = 90*

FIGURE 185.—Approach angle as influenced by depth adjustment with a radial linkage system. of tillage tool design. The interaction should also stimulate the desire for quantitative relations to represent the interaction, so optimum designs can be developed ( 4^4 ). 5.4.2 Path of Motion Path of motion or travel is the second element involved in specifying the abstract design factor, manner of movement T^. Path of motion is the path the tool travels when passing through soil. Fol- lowing the approach used for the description of orientation, an obvious means of description is to specify the path of travel in mathematical terms. The path of the shape coordinate system may be followed in a fixed coordinate system in which the tool is considered to move. A logical choice for a fixed coordinate system is the so- called earth system, which is fixed with respect to the planet earth. Although the simultaneous mathematical specification of two coordinate systems seems complicated, the path of motion description usually simplifies to a statement of the depth and width of cut of a tool. All tools that travel in straight lines can be described by this technique. Only rotating and oscillating tools have paths of travel that require relatively complex mathematical descriptions. Because of the simplicity of specifying the path of motion of tools traveling m a straight line and because of the difference between these tools and rotating or oscillating tools, only straight line path of motion tools are discussed in this section. For a tool that operates in a straight line the path of motion through soil is usually specified completely by the depth of cut and width of cut. Both depth and width are readily changed, and they are the means used most often to "adjust" design when the force required to move the tool is greater than can be easily supplied. Most tools can be operated in a specified range without too greatly affecting their manipulation of soil. Forces have been studied because they have often been the limiting factor when a tool is used. Thus, considerable data are available concerning the effect of the depth and Avidth of cut on draft ( i^ ). Their effect on resulting soil conditions has not been studied in nearly as great detail. In a uniform soil condition, the draft of a tool almost universally increases with increasing depth or width of cut. Data in table 26 reported by Kynazev ( 236 ) are typical. Since most tillage tools are designed to operate in a specified range of depth and width of cut, the specific draft (draft per unit of cross-sectional area) is often used to reflect the effects of path of motion on draft. The specific SOIL DYNAMICS IN TILLAGE AND TRACTION 261 iraft of a 14-inch moldboard plow in several soil conditions is shown in figure 186 ( SU, 350 ). The data indicate that depth of operation 3an be increased up to 5 inches in most soil conditions without an appreciable increase in specific draft.

~~24 HOUSTON CLAY~~

~~20 ^-SHARKEY CLAY c 16 OKTIBBEHA CLAY~~

~~VAIDEN CLAY~~

~~Û SHARKEY LOAM I 8 Ü ÜJ NORFOLK SAND OL if)~~

~~DEPTH (in)~~

~~FIGURE 186.—Effect of operating depth of a moldboard plow on specific draft. (Randolph and Reed, Agr. Engin. {SU).)~~

Table 27 shows the effect of varying width of cut while maintaining constant depth on the specific draft of a moldboard plow bmce the shape of a moldboard plow is complex, varying its width o± cut changes the path soil takes as it moves over the surf ace of the plow. Thus, the shape of the tool is also changed as the width ot cut is varied. Limited data indicate that only a slight change in specific resistance occurs. More data are required before any definite trend can be established.

~~TABLE 2^,—Increase in draft of a ftve-hottom chisel plow due to increases in depth of operation~~

Depth of Draft per unit operation Draft force width of disturbed (centimeters) soil Kilograms Kilograms/Centimeter 5.1 8.3- 507 1,259 13.3 18.3- 21.3 28.3- 2,159 3,264 30.4 33.6- 33.2 35.2- 3,338 4,334 39.6 40.6- 42.1 43.8- 5,200 SouRE : Kynazev ( 2S6 ). AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~TABLE 27.—Effect of width of cut of a 12-inch moldhoard plow on the specific draft in a sandy soil~~

~~Width of cut by plow Specific draft (inches)! of I)1()\V P.s.i. 8 2.0 10 2.1 12 2.1 14 2.1 16 2.2 1 Depth of cut wa.s constant. SOURCE: Randolph and Reed ( SU ).~~

No indication of effect of path of motion on the results of soil manipulation (ñnal soil condition) were reported for eitlier of these studies. (îill and McCreery ( H9 ) reported on the amount of soil breakup as affected by widtli of cut. Fisrure 187 sliows sections of

FIGURE 187.—Sections of a nioldboard plow u.sed to vary the width of cut. (Gill and McCreery, Agr. Engin. ( IJ,!) ).) a moldboard plow that were used to vary width of cut. Shape was inadvertently varied to the extent that different finite areas of the same shape were used to vary width of cut. Thus, there may be an unavoidable interaction between sliape and manner of movement in the results. Table 28 shows that as width of cut increased, clod size also increased. The data also show that specific draft generally tended to decrease as size of cut increased. Since lower specific draft indicates a lower force per unit of cross-sectional area, the increase in width of cut would appear to be advantageous. On the other hand, if a high degree of pulverization is desired, the smaller width of cut is advantageous. The separate yet simultaneous nature of equations 1.32 and 13,3 is revealed in the results of this study. Gill and McCreery proposed a way to consider the two contradic- tory trends by calculating the energy api)lied to the soil for each width of cut. They calculated the energy from draft and speed SOIL DYNAMICS IN TILLAGE AND TRACTION 263

~~TABLE 2^,—Effect of size of cut on the utilization of energy in pulveHzing soil~~

~~Equivalent Clod Energy energy mean- Specific Size of applied to required to Efficiency weight draft cut soil by tool cause soil of tool diameter (WJ breakup (inches)~~

P.s.L Inches Ft.-lh./cu. ft. Ft,-lh./cu. ft. 1.47 . 27.7 1 2,256 1,790 0.79 3.55 16.0 2 1,302 855 .65 6.46 10.8 4 876 290 .33 7.07 _ _ -. 11.7 6 946 239 .31 8.61 12.1 8 979 137 .14 SOURCE : Gill and McCreery {149 ). measurements on a unit volume basis, as indicated in table 28. They also determined the equivalent energy required to cause soil breakup by using a drop-shatter technique (sec. 3.3.1). A large continuous block of soil was dropped, and the potential energy involved m the drop (mass and height of drop considerations) was termed the equivalent energy that produced the resulting soil breakup. The mean weight-diameter clod size was determined after measuring clod sizes with a rotary sieve. Following a succession of drops, a mean weight-diameter clod size-equivalent energy curve could be constructed for the soil condition being considered. The equivalent energy for any clod size produced by a particular width of cut could be determined from such a curve. The ratio af the equivalent energy to the energy applied to the tillage tool can be considered a measure of the efficiency of the tool. As the data in table 28 indicate, the small width of cut was much more efficient than the larger width of cut. Consequently, the high specific draft of the small width of cut is not a penalty if the soil must be further tilled to produce a small clod size. The conclusions reached by Gill and McCreery cannot, o± course, be considered final. Their work does indicate, however, the importance of path of motion on the resulting soil manipulation. Furthermore, the work clearly demonstrates the necessity of simultaneously considering both design equations. If only the relation between force and path of motion were considered in table 28, a large width of cut would seem to be superior. Simultaneous consideration of soil breakup provides information that completely re- verses the apparent trend. Certainly more work is required to verify or to modify the conclusions of Gill and McCreery. 5.4.3 Speed If the orientation and path of motion of a tool are known, the manner of movement will be completely determined if speed is specified. Specification of speed is simply describing the velocity of the tool or, in a more general sense, the velocity of the shape frame of reference along its path of motion. When the path of motion is a straight line, speed is easy to express. The mathematical representation of speed for rotating and oscillating tools 264 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE is also simple if the path of motion is simple. When velocity is not uniform, it must be quantitatively expressed at each point along the path of travel. Because of the considerable difference between tools traveling in straight lines and those traveling in more complicated paths, only straight line paths of travel will be discussed in this section. When sufficient power is available, speed is the easiest design factor to vary. In practice, speed often is varied. The effect of speed for straight paths of travel has been widely studied. Unfortunately, nearly all researchers have considered only the relations between force and speed. Since the effect of speed on draft is large, it is of practical importance. As one might suspect, an increase in speed increases draft ( 4^5 ). This trend has been sufficiently consistent so that quantitative relationships between speed and draft have been obtained. McKibben and Keed ( 278 ) have generalized this trend trom a considerable amount of data in an approximate equation D = k{v-3y-^, (143) where D = draft in pounds, V = speed in m.p.h., k = coefficient varying from 5 to 15 depending upon tool. Others ( 27 ) have expressed the same type of data in the form

~~^ = 0.83 + 0.0189 ^2^ (144)~~

where D^ = draft at speed v, Z>3 = draft at 3 m.p.h., V = speed in m.p.h. Garbotz and Drees ( 1S8 ) have concluded that an approximate relation might be m the form ^ = Dov, (145) where D = draft. Do = base draft for a specified speed and soil condition, V = speed. Soehne {40S ) recently used an equation of Goryachkin's to express draft and speed relations of tillage tools. The equation is D = Do + €v^, (146) where D — draft. Do = basic draft independent of speed, V = speed, € = a constant. The quantity €v^ was considered to be a dynamic component of the relation. The component has the same general form as the fluid dynamic factor pv^ where p is fluid viscosity. While the components may be analogous, e and p probably are not analogous. For moldboard plows, Soehne found the magnitude of e ranged from 0.95 for hehcoidal-shaped plows to 3.67 for digger-shaped plows SOIL DYNAMI<:S IN TILLAGE AND TRACTION 265 The draft-speed relations expressed in equations 144 through 146 show that quantitative design equations can be developed. Obvi- ously, these three equations are highly restricted. As discussed m section 5.2, however, even design equations developed from basic behavior equations ( 213 ) will be restricted by the assumptions and limitations that are incorporated. ^ - ^ A When empirically developing design equations, a logical order for study seems apparent. Since shape is the most difficult abstract design factor to vary, perhaps that factor should be the first to be quantitatively developed rather than some other, such as speed. Although speed can obviously be quantitatively related at least to draft, the relation is probably not the most useful one for design purposes. ^ xi x i. The manner in which tillage tools are used suggests that shape is the most important design factor to be considered. The ideal tool produces the desired soil manipulations in a variety of soil conditions. The user can most easily control soil manipulation by changing the manner of movement of the tool, such as depth, speed, and width of cut. Furthermore, he usually has a certain limited range within which the tool must be operated. A practical range tor plowing may be from 5 to 8 inches deep and from 3 to 5 miles per hour. If quantitative shape-design equations were developed tor depth of operation and speed within this range, shape could be truly designed for these restricted conditions. The effects of depth and speed for a suitable shape could then be determined or, as a stopgap measure, the effect could be expressed as modifiers of shape. Ulti- mately, equations 132 and 133 must be fully developed. In empirically developing these equations, certain priorities seem logical. From a practical standpoint, quantitative shape-design equations would seem to be more useful than manner of movement equations. Hence, shape should receive first priority even though speed or depth relations can be more easily obtained. 5.5 Multipowered Tools Multipowered tools as defined here are tools that obtain the energy required to move them through soil in more than one manner. Ihe power need not be supplied by more than one source of energy ; but the energy, regardless of the source, must be applied to the tool m more than one manner. The first means of applying power to tillage tools, and the one still most widely used, is simply to draw or pull the tool through soil. Tools mounted on modern tractors are powered by this method. Kotating and oscillating tillage tools are examples of multipowered tools. Draft energy and rotating energy are applied to these tools. Two primary reasons exist for using the more complex mechanisms required for multipowered tools. First, draft requirements are generally reduced. In fact, under some circumstances rotary tools actually propel themselves through the soil. Among the many advantages of reducing draft is the important one of reducing traction requirements of the associated prime mover. The second reason tor using multipowered tools centers on their ability to manipulate soil in a desired manner. A rotary tool of suitable design offers a 266 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE wide range of possibilities for changing the path of motion. Changes in movement greatly affect the final soil conditions that can be created. While many other subtle effects may be considered when comparing drawn and multipowered tools, most can be roughly categorized under one of these two reasons. From a soil dynamics standpoint, the principles of design for a multipowered tool are no different from those for a simple drawn tool. Shape, manner of movement, and initial soil condition are the three independent abstract design factors that control the forces required to manipulate the soil and create the final soil condition. Use of different shapes and vastly different manners of movement, which are possible only with multipowered tools, will result in different forms for equations 132 and 133. The forms of these equations will reflect the differences that are due to descriptions of shape and manner of movement but not a difference in principles. The differences originate from the restrictions or limited application of the particular design equations that are imposed by the shape and manner of movement, not from the manner of powering the tool. Consequently, all design principles discussed in sections 5.3 and 5.4 will also apply to multipowered tools. Several types of multipowered tools have been developed and examples will be discussed. 5.5.1 Electro-osmosis Many years ago it was established that water moves from a positive to a negative pole when an electrical potential is applied across a finite volume of soil. Under certain circumstances, some soils respond in >n opposite manner and water moves to the positive pole ( ^4 ) ; In either case, the phenomenon has been termed electro- osmosis, and the possibility of moving water that is present in soil to the soil-tool sliding surface suggests the possibility of changing the frictional resistance offered to sliding. Obviously reduced draft, better scouring, and reduced wear make the application of electro- osmosis to tillage tool design worthy of consideration. The principles of electro-osmosis are understood ( 6i, 153 ), but the principles of how water movement affects friction and hence tillage tool designs are not known. Lack of fundamental knowledge of soil behavior rather than of the phenomenon of electro-osmosis prevents incorporating electro-osmosis into quantitative design equations. One of the concerns about using electro-osmosis to reduce sliding friction is the amount of electrical power required to move significant amounts of water. The value of the power in transferring water, however, depends on how the water affects sliding friction ; the friction, in turn, depends on several soil factors. Thus, the situation is somewhat analogous to a heat pump, where its effectiveness depends more on the temperature difference between the sink and the source than it does on the energy required to physically transfer the heat. Figure 188 shows that the amount of electricity required to move water through soil can vary considerably ( 260 ). Because of the question of the amount of energy involved, the total energy supplied to tillage tools utilizing electro-osmosis has been studied. Shirokov ( 385 ), using electro-osmosis on a disk plow under field conditions, reduced total power approximately 15 percent (table 29). Weber ( 499 ) and later Wu Hung-Chein ( 513 ) also reported that SOIL DYNAMICS IN TILLAGE AND TRACTION 267 400-1 E o

~~5:^300-~~

~~^ 200 H O UJ~~

~~100~~

~~20 40 60 80 CLAY CONTENT {%)~~

~~FIGURE 188.—Effect of clay content on the energy required to move 1 cubic centimeter of water through soiL (Maclean and Rolfe, Philos. Mag. (260).)~~

the process may be utilized effectively on tillage tools operating under field conditions. Shirokov also demonstrated that mcreased speed reduces the effectiveness of electro-osmosis, particularly at speeds above 1.5 meters per second (fig. 189). Paired curves at pomts A and B represent two soil conditions. The data m table 29 and m figure 189 indicate that electro-osmosis can produce practical decreases in draft. • v i. j Not all studies of electro-osmosis on tillage tools have mdic^ed a sis-nificant response under field conditions. Crowther and Hames ( 89 ) were unable to obtain a field response, but they were able to demonstrate the effectiveness of the process on simple sliders. Since electro-osmosis affects only sliding friction, several ^^searchers have concentrated on relations between electro-osmosis and sliding friction. Dano ( 93 ) found that simple relations do not exist between soil conditions and the effectiveness of electro-osmosis. He utilized a slider to supply the frictional interface and reported that low normal loads (1 p.s.i.) do not provide sufficient contact between the soil and the sliding surface. At normal loads of 2 and 3 pounds

~~TABLE 29.—Effect of a 100-volt electrical potential on the foioer requirement of a dish j)loiö operating at 2.6 kilometers per hour~~

Mechanical power Son Mechanical power plus electrical Savings used for plowing power used for in moisture without electro- power (percent) plowing with osmosis electro-osmosis Horsepower Horsepower Percent 14.0 26.6- 28.8 24.6 23.4 19.6 16.2 24.5_ 10.4 17.9- 18.0 16.1 SOURCE : Shirokov {385 ). 268 AGRICULTURE HANDBOOK 316. U.S. DEPT. OF AGRICULTURE

~~1000 < Q 800~~

600 —1— .8 1.0 1.2 1.4 SPEED (M/sec) FIGURE 189.—Influence of speed on the effectiveness of electro-osmosis in reducing plow draft. Solid lines, Draft values without electro-osmosis ; dotted lines, draft values with electro-osmosis. ( Shirokov, Zhur. Tekh. Fiz. ( S85 ). )

per square inch, friction was more effectively reduced with electro- osmosis. Dano concluded that the volumetric moisture content of the soil was ih^ measurement that most closely indicated the effectiveness of electro-osmosis. Mackson ( 286 ) used a simple slider to investigate electro-osmosis through voltage ranges of 50 to 300 volts and speeds of 2.5 to 300 feet per minute. He determined an equation for a clay loam soil that related the influence of various factors on the draft of the slider. The equation had the form D = 2.83 + OmUS - 0.00708F - OMIM + 0.514P, (147) where D draft of slider in pounds, S speed in feet per minute, V potential in volts, M soil moisture content in percent, P normal force in pounds. Several conclusions can be drawn from the various studies of electro-osmosis. Its effectiveness in reducing draft seems to hinge on the following conditions : 1. Sufficient electrical potential must be applied to cause water movement. 2. The soil must be permeable enough for rapid water movement. 3. Sliding must occur at the soil-tool interface. 4. Good contact must exist through the soil. 5. Sufficient time must be allowed for w\ater to move. 6. The ratio of friction to total draft force must be large so that the ehmmation of friction would be significant. These conditions are sufficiently restrictive so that the application of electro-osmosis will have to be specialized rather than general. Available data indicate, however, that there are large areas in the world where the principle may be expected to work. Nearly all studies have been concentrated on reducing draft; but, an indirect ^ctor that must also be considered is reduced traction requirements. Even when draft can be reduced only with an increase in total power, traction requirements may make electro-osmosis practical or econom- SOIL DYNAMICS IN TILLAGE AND 'ÏRACTION 269 ical. Keduced traction requirements may reduce expensive traction equipment requirements, particularly since electro-osmosis seems to be most effective in moisture ranges where traction capacity is severely limited. More knowledge, however, is required before electro-osmosis can be quantitatively included in design so as to predict its effectiveness. 5.5.2 Rotating Tools Three reference systems are needed to describe paths of motion of rotating tools: (1) The earth reference system is a logical and most convenient fixed system; (2) the implement reference system is fixed with respect to the framework and mechanism that permits thé rotary motion; (3) the shape reference system is the coordinate axis m which the shape is described. Thus, the shape reference system moves in a circular path in the implement reference system (sec. 5.4.1), and the implement reference system moves (usually in a straight line) in the earth reference system. In this publication a tillage tool that moves with circular motions is defined as a rotating

The designed control of the manner of movement of a tool through soil is the most outstanding characteristic of a rotating multipowered tool. Energy is applied to the implement to cause movement of the shape reference system in the implement reference system as well as in the earth reference system. In this manner, draft energy as well as rotary energy is supplied to the implement. Control of manner ot movement results from the independent control of the movement o± the shape and implement reference systems. Their combined paths of movement give the actual path of movement of the tool through soil. The actual path of travel is, of course, the path that is observed in the earth system. Figure 190 shows two paths of travel that can result from varying either the speed of the implement reference system or the rotating speed of the shape reference system {i05). The action shown in figure 190, B inverts the slice after it is cut loose since not only the path of movement but also the shape of a tool can be varied. Rotating tools offer many possible means for increasing control to obtain the desired soil manipulation.

~~(A) (B)~~

FiGUKE 190.—Effect of two paths of tool travel on soil manipulation. ( Soehne and Eggenmüller, Grundlagen der Landtechnik (^Ö5).) 270 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Many arrangements and configurations have been used for multipowered rotating tools. Davidson and Collins built a number of multipowered machines and described them as early as 1929 {9^), A nuniber of movements were reviewed by Fischer-Schlemm and Moser in 1953 ( 118 ), and the extreme versions are shown in figure 191. Most of the machines whose principles are illustrated were invented or designed from intuition rather than from basic principles; nevertheless, some have been successful tillage tools.

~~FIGURE 191.—Various configurations of rotating tiUage tools. (Fischer- Schlemm and Moser, Landtechnische Forsch. {118).)~~

Magazines such as Farming Mechanization ( 115 ) contain many designs of multipowered tools that provide motions other than those shown m figure 191. Because a circular path is easily described mathematically and is simple to obtain from a mechanical standpoint, rotary systems are identified as a widely used special category. This section is restricted to a discussion of rotating tools, since the principles involved in describing the action are the same regardless of the particular path that the shape reference system makes in the implement reference system. Design equations for rotating tools must be based on the same principles used in developing equations 132 and 133. Shape of the tool and manner of movement must be described and quantitatively related to the appropriate dependent functions F and Sf (sees. 5.3 and 5.4). Shape must be mathematically described along with orientation, path of travel, and speed. These last three quantities require more definition for rotating tools than they do for tools that travel m a straight line. For the latter, the shape and implement reference systems coincide so that they can be reduced to one reference system. For rotating tools, the two reference systems do not coincide; and the SOIL DYNAMICS IN TILLAGE AND TRACTION 271 orientation, path of travel, and speed of each reference system must be individually specified. Since the implement reference system usually travels in a straight line, the added complexity of the mathematical description is not as great as it first appears, and the simultaneous consideration of three reference coordinate systems is prac-

Of the various proposed systems of rotating tools, those similar to the one shown in the upper left of figure 191 appear to be most successful. In this arrangement, the axis of rotation of the shape reference system is a line perpendicular to a vertical plane containing the direction of travel. The implement is made up of a number of similarly shaped tines appropriately spaced along and around the axis of rotation. Tool macroshape refers to the shape of an individual tine rather than the ''shape" of the implement. Since numerous tines are used on a rotary tiller (the implement), a detailed description of macroshape of tines has not seemed to be too important. Also, when used at high speeds of rotation, shape probably has not been as important as other factors such as arrangement of the tmes on the implement. Nevertheless, shape ultimately will need to be quantitatively described. Adams and Furlong ( 1 ) have studied several macroshapes tor rotary tillers. They did not describe the shapes mathematically, but depicted them graphically (fig. 192). They determined power re-

~~B HOE SLICER PICK~~

~~FIGURE 192.—Typical shapes of rotary tiUer tines. (Adams and Furlong, Agr. Engin. {!).)~~

quirements, in terms of both rotary and draft energy, for each shape as well as qualitative results of soil manipulation. Thus, they considered both design equations even though sometimes they used qualitative characterizations. A summary of their findings is shown m figure 193. Of the three tine shapes, the so-called hoe seems to be superior in nearly every consideration. The dotted lines m figure 193 represent the range of power requirements for small changes ot the macroshape with no change in the basic configuration Many workers have established the apparent superiority of the hoe tme. 272 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE HOE 4 - SLICER PICK 3 I ROTOR HORSEPOWER 2 I

TRACTOR HORSEPOWER fl! H H -I 400 AVERAGE HORIZONTAL 200 FORCE (FORWARD) -200 I AVERAGE VERTICAL FORCE (UPWARD) "400 -600 I I -800 4 i PULVERIZATION (AVERAGE CLOD SIZE) 2 1 DISPERSION OF 1 FAIRLY EVEN MOSTLY IN UPPER SURFACE RESIDUE FAIRLY EVEN HALF OF BED CHOPPING a WINDING GOOD CHOPPING FAIR CHOPPING OF SURFACE RESIDUE POOR CHOPPING NO WINDING NO WINDING SEVERE WINDING FAIRLY HARD SUB-BED CONDITION FAIRLY LOOSE LOOSE WITH AND SMOOTH WITH RIDGES SPACED FURROWS

~~FIGURE 193.—The effect of shape of rotary tiller tines on various measures of performance. (Adams and Furlong, Agr. Engin. ( 1 ).)~~

and it IS widely used on rotary tillers. Japanese manufacturers have utilized curved-knife, or so called Nata-Tume, tines to an increasing degree {U5), For special purposes, special shapes may be superior to the hoe-shaped tine. The configuration and arrangement of tines about the rotor create restrictions as well as possibilities regarding the manner of movement of an individual tine. Drawn tools traveling in straight lines pass through the soil in a series of consecutive parallel paths. A moldboard plow inverting soil into the furrow created by its previous passage is an example. This path arrangement is not always practical, or even possible, for the tines on a rotary tiller. Soehne ( 399, 4,06 ) has studied some of the implications of tine arrangement. ^ Figure 194 shows some boundary conditions an individual tme might encounter when the tines are viewed just as they enter the soil. Only D, E, and G are practical types of cuts since the others require either varying lengths of tines or immobility of the implement. The comparative torque requirements indicate that the energy requirements depend on either the geometry of cut or the shape of an individual tine. Soehne conducted studies of these boundary conditions by using a special apparatus with which a single tine could be revolved and passed once through soil at a controlled speed. By measuring the torque required to till soil in each of the various boundary conditions (fig. 194), he was able to separate the torque requirements into cutting and shearing components. The ''piece" of soil that is separated SOIL DYNAMICS IN TILLAGE AND TRACTION 273

~~(A) (B) (C) (D) (E) (F) (G)~~

~~2.0 KgM 3.0 KgM 3.0 KgM 3.8 KgM 4.2Kg^fl 5.2 KgM 6.5 KgM~~

~~FiGUKE 194.—The effect of the geometry of cut on the average torque required to move a hoe-shaped tine through soil. (Soehne, Grundlagen der Land- technik ( 399 ).)~~

from the soil mass is very nearly the same size for each soil-tool boundary condition. The proportion of the total area that is cut by the hoe and the proportion of the total that is sheared from the soil mass differs for each condition. Condition A, for example, has no shear and it has the least area requiring cutting of all the conhgura- tions Condition F, on the other hand, has no shear but it does have the maximum area requiring cutting. Condition B has the same area requiring cutting as condition A in addition to maximum shear. Condition G, on the other hand, has both maximum cutting and maximum shear. A comparison of the average torques m figure 194 indicates that shearing requires less energy than cutting. Cuttmg is constant in conditions C, D, and E; but shearing increases progressively from zero in condition 0 to the maximum possible in condition E and the average torque decreases as shearing area decreases, ihe same conclusions may be reached by comparing conditions A with B and F with G. Furthermore, as the ratio of shearing area to cutting area decreases, the etfect of shearing on the total required torque decreases. Even though the lateral shearing area in condition B is much greater than the cutting area, data m figure 194 show that torque values in A are approximately only 67 percent of those m B. The cutting area is greater than the shearing area in condition O- yet the torque in condition F, which has no shear, is approximately 80 percent of that in G. A comparison of conditions B and £", where the ratio of shearing area to cutting area is nearly equal, shows that the torque in B is approximately 71 percent of that in A. it the cutting and shearing components of the total torque were equal, condition B should require more than twice the torque ot condition A. Similarly, shearing should have a greater influence m the other conditions if shearing and cutting were equal. Thus, shearing soil appears to require less energy than cutting. .. . A +;„oa Soehne also studied macroshape and orientation of hoe-shaped tmes with the same experimental apparatus. He expressed measured torque values on the basis of the volume of disturbed soil (size ot the piece) in order to evaluate the energy requirements on a specific work basis. He calculated the specific work by dividing the average torque by the volume of disturbed soil. Figure 195 shows some of the tool parameters that he studied. He did not describe the exact shape ot each tool; but the radius R and width W are parameters that reflect 274 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~CUTTING ANGLE~~

~~R = RADIUS .RAKE ANGLE O O~~

~~(A) (B) (C)~~

~~FIGURE 195.—Shape and orientation parameters of hoe-shaped rotary tiller tines. (Soehne, Grundlagen der Landtechnik { 399 ).)~~

shape characteristics. He described the orientation of the shape with respect to its path of travel by the angles identified in figures 195, B and 0. Data in table 30 show the effect of the shape parameters W and R on the specific work required to make two types of cuts (for conditions D and 7^ in fig. 194). The total area of soil to be separated IS the same for both conditions. In D, however, the total area was equally divided between shearing and cutting, whereas in F the total area was for cutting. Shearing required less energy than cutting. As the width of the tine was increased, the specific work required to pass the tme through the soil decreased. Since no measure of soil breakup withm the detached mass of soil was reported, the extent of the total work on the soil is unknown. The importance of simultaneously considering both design equations in greater detail is thus emphasized. Eesults in table 30 indicate that changes in radius above 30 millimeters appear to have little effect on the specific work required, but changes in radius below 30 millimeters can significantly increase the specific work required. As a result, trends between the shape parameters IÎ and W and work requirements are clearly indicated. The effect of orientation parameters on specific work requirements was also studied by Soehne. He used single hoe-shaped tines, which

~~TABLE SO.—Effect of the loidth and the radius of curvature of a tine on the specific work performed on the soil, for two types of cut~~

Tine measurement Type of cuti (millimeters) (D) (F) Width (TF)2 Kg, -m./dmß Kg.-m./dmß 85. 9.0 12.0 55_ 7.5 10.3 75___ _ 6.2 9.6 95_ 6.0 9.5 Radius of curvature 15__ 9.0 10.2 30_ . _ 7.0 8.0 50 _ — — 6.5 8.0 1 Types of cuts (D) and (F) are shown in figure 194. 2 Width (W) and radius (R) are shown in figure 195. SOURCE : Soehne (399 ). SOIL DYNAMICS IN TILLAGE AND TRACTION 275 he passed through the soil once. The rake angle (fig. 195, B) has no significant eíTect on specific work over a range from 50° to 80 , whereas the cutting angle (fig. 195, C) seems to have considerable effect Data in table 81 indicate that minimum energy is required at approximately 20°. The cutting angle 8 (fig. 195, G)_ cannot be considered by itself since the clearance between the tine and the soil is also present. Figure 196 shows the relation between the clearance angle a and the cutting angle 8 for a rotating tool. The tine angle of sharpness

~~/ / I /~~

~~\ \ \ \ N~~

~~FIGURE 19G—A, Relation between clearance angle a and the cutting angle 8 of a rotary tine; B, cutting and clearance angle correction associated with forward implement velocity u,.~~

was 10° SO that a cutting angle of 15° provided a clearance angle of 5° Soehne concluded that the increase in specific work occurring at low cutting angles results from added friction along the back side of the tine He further pointed out that because of forward movement of a rotary tiller implement (Soehne's experimental apparatus did not move forward), both the cutting and the clearance angles are decreased since the tool actually travels in a cycloid path rather than in a circle. The path is circular in the implement reference system where the angles 8 and a exist as shown m figure 196, ^y but the path is cycloidal in the earth reference system. Since velocities in moving reference systems add vectorially, the two velocities (tool velocity in the implement reference system v«, and the velocity ot the implement reference system in the earth systeni vj) can be added to give the tangent to the actual path of travel. Figure 196, tí shows the decrease in clearance and cutting angles A8 tor a single position of a tine in a forward-turning rotary tiller. Since the tool velocity vector changes direction as the tool moves m its circular 276 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE path, the relation between the actual cutting angle and the angle correction factor A8 ranges from zero where the implement and tool velocities are parallel to a maximum where they are perpendicular. The relation shown in figure 196 can be used in either graphical or analytical methods to determine true cutting and clearance angles for any combination of speeds and depths of operation.

~~TABLE ?>1.—Effect of the cutting angle of a tool on the specific work required for cutting soil loith two types of cuts~~

Cutting angle Type of cut2 of tool (degrees)! (D) (F) Kg.-m./umß Kg.-m./äm.^ 15 9.5 8.5 19 7.0 7.6 25 7.0 8.2 30 _ _ _ 8.2 9.2 1 Cutting angle (ô) is shown in figure 195. 2 Types of cuts (D) and (F) are shown in figure 194. SouKCE : Soehne {S39).

Soehne also investigated the influence of speed on average torque as the tool passes through the soil. Single hoe-shaped tines were compared when cutting in conditions D and F, as shown in figure 194. A definite trend was established between decrease in average torque and decrease in circumferential speed. A reduction in circumferential speed from 5.2 to 2.6 meters per second reduced the average torque 23 percent in condition F and 42 percent in condition D. Over the range in which Soehne varied speed, the decrease in average torque with decreases in speed was nearly linear. As shown m section 5.4, the force required to move a tool through soil always decreases with decreased speed so that the tool should be moved through the soil as slowly as is practical. In a rotary tiller, however, decreased peripheral speed at a constant forward speed decreases the actual cutting angle so that compromises must always be eiiecteci. ^ Soehne's work concerning design factors of individual hoe-shaped tmes is to be commended. He has quantitatively related descriptive parameters of shape and manner of movement to forces in a form compatible with design equation 132. No equations were actually developed, but quantitative relations are established by the data. All measurements were made in one soil condition that was obtained m a laboratory soil bin.. The soil was described as a fine sandy loam with an average moisture content of 16.5 percent and an average pore space of 49 percent. Until additional results are determined tor a variety of other soil conditions, the trends indicated by these data cannot be generalized. As a result, equations based on available information would be too highly restricted to have practical value. Also, Soehne's report does not reflect a relation with final soil conditions (tillage equation 133). Until such information is also available^, only part of the required design information is available. Thus, Soehne's work contributes significantly to the attainment SOIL DYNAMICS IN TILLAGE AND TRACTION 277 of design information, but it is just a beginning upon which much more must be built. . . • n 11 The torque on an individual rotating tme varies considerably as the tine cuts a slice of soil. Figure 197 shows typical torque curves

~~Umax'ZB6Mm~~

~~1+2'~~

~~r+2 r+2~~

~~1 + 2'~~

~~90» 180«~~

FIGURE m.-Effect of number and location of tmes «", tofX " 2 HnP roíor rotor with tines operating as pairs in tlie same row ; bottom, 12-tine rotor with Tines equally spaced around the rotor. (Soehne, Grundlagen der Landtechnili (399).)

for one tine 31 and two tines 231 passing through soil. For a rotor of the usual diameter operating at the usual depth, all soil resistance is encountered in a 90°-angle of rotation. As figure 197 shows, peak torque 31 „a. and average torque J/,„ for an implement can diner greatly because of the arrangement of the tmes about the rotor. Proper spacing can decrease the variation in amplitude of torque to provide a smooth and desirable torque pattern. Increasing the number of evenly spaced tines on a rotor produces a snioother torque curve. Also, with more tines on a rotor, the peripheral speed can be reduced while, the size of the soil slice is maintained tor a given forward speed. On the other hand, spacing tmes too closely causes clogging, and slower rotating speeds decrease cutting and clearance angles. Any final arrangement and spacing of tmes, therefore, becomes a compromise. . í . ^;n<,^ Figure 198 shows the effect of three arrangements of rotary tiller tines on cut and torque patterns. The technique shown m figure 198 is one means of evaluating the geometry of cut for any particular tine arrangement. Careful examination of figure 198 shows that individual tines can have different boundary conditions, depending on the arrangement. For example, in some tine arrangements, the 278 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~180°-,~~

~~^ 90~~

~~T 1 r- 12 3 4 5~~

~~Mmax = 1.22 Mm r rl.l7Mm ,V'/v\^^^vV^v\~~

~~FIGURE 198.—Effect of arrangement of rotary tiller tines on cut and torque pattern. (Soehne, Grundlagen der Landtechnik ( ^9P ).)~~

actual size of the soil slice differs for different tines. Even if the size of the slice is constant, the nature of soil failure along the boundary may vary. Detailed consideration of soil-tool geometries shown m figure 198 shows that the cutting and shearing areas of a soil slice vary from tine to tine. Unless the rows of tines run parallel to the rotor axis, the cutting and shearing areas for individual tmes cannot be made to be identical. Interior tines shown in the flat spiral arrangement at the left of figure 198, for example, have shearing areas of soil slices that alternate between 40 and 60 percent of the length of cut—that is, the shearing area of an external tine. Ine steep spiral arrangement at the center has a shearing area that alternates between 20 and 80 percent of the length of cut. The unbalanced arrangement at the right, which lets the two external tmes strike at the same time, should be avoided. In spite of the variation m shearing area for the steep spiral, its arrangement is a suitable compromise of all factors. In addition to the gross arrangement of tines around and along the length of a rotor, the "microarrangement" of tines is important. ± igure 199 illustrates how the microarrangement of individual tools may be varied to control overlapping and to improve performance Arrangement C requires the least power; arrangement A, the greatest. A careful examination of the geometry of cuts in figure 199 shows that arrangement G tends to minimize the drag between an individual tme and the soil slice that is cut loose. The frictional drag IS minimized because the overlapped tine moves along an area where the soil slice has already been largely formed by the passage SOIL DYNAMICS IN TILLAGE AND TRACTION 279

~~(A) (B) (C)~~

FIGURE 199.—Overlapping of rotary tiller tines to minimize drag. (Soehne and Thiel, Grundlagen der Landtechnik { 406 ).) of the previous tine. The overlapping of cuts is just one of many microarrangement factors that must be considered when tmes are arranged as a group on rotary tillers. , Soehne ( 399) formulated the following general requirements tor arranging tines on a rotary tiller: . 1. The angular distance between tines as they successively penetrate soil must be kept constant, and no two tines should strike the soil simultaneously. . ^ .. ^ ^ j 2. To prevent clogging, the circumferential distance between aa- iacent tines should be maximized. « , i 3 Tines located to the right and left of the center of the longitudinal rotor axis must strike the soil more or less symmetrically to minimize unequal mom.ents. P . T -i i x- 4. The area of shearing and cutting surfaces of individual tmes must be balanced with the idea of creating equal torques. The best design of a rotary tiller will be the one that eftects the best compromise of these four requirements. In closing the discussion of rotating tillage tools, recognition must be made of the wealth of information in Japanese literature. Fundamental studies of rotary tillers have been published by -Doctors M. Tsuchiya and M. Matsuo of Yamagata University ; Dr. N. Ka- wamura. University of Osaka Prefecture; Dr. S. Umeda, Kyoto University; and others; but the difficulty of securing translations tor the Japanese language has prevented thorough use of the material. 5.5.3 Oscillating Tools Oscillating multipowered tillage tools are tools that move the shape reference system in a path that swings within the implement reference system. Any distinction between rotating and oscillating multipowered tools is only in the path of motion, not m the method or principle of energy application. Interest in oscillatmg tools has risen because of reports that the use of oscillations has reduced draft requirements of tools. Paths of oscillation may be controlled by mechanical means such as eccentrics, cams, or crankshaft and connecting rod arrangements. These mechanisms provide the means for applying oscillating energy to the tool as it is being drawn 280 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE through the soil. Design information for oscillating tools will be similar to that for rotating tools. Parameters of the manner of movement and shape need to be related quantitatively to forces and final soil conditions. A spring tine is a practical oscillating tool that is not multipowered and that has uncontrolled oscillations {303, 424,), The oscillations are induced by variations in soil resistance. When high resistance is encountered, the tine displaces; when resistance decreases, the restoring force of the spring returns the tine to its original position. Presumably, oscillation of a flexible tine permits the tool to take advantage of minor irregularities in soil strength. Möller ( 303 ) found that the draft of spring tines may be 20 to 30 percent less than the draft of rigid tines. The two types of tines were equally effective in breaking up soil. The extent to which the depth of operation may be affected must also be considered in evaluating performance. Although a spring tine is not a multipowered tool, it shows how an oscillating path can reduce draft. The exact reasons why a controlled oscillating tool may require less draft are not known. All tillage tools that have been discussed so far have had reasonably uniform paths of motion through the soil. Furthermore, the speed of the tool along the path of motion has been uniform. Even rotating tools have had uniform motion. The very nature of the swinging motion of an oscillating tool requires changes of both acceleration and speed. Thus, the force re- miirements of a tool used on a specified path of travel may change if an oscillating motion is superimposed on the basic path. Kondner ( 226 ) demonstrated this fact by vibrating small cutters as they penetrated soil. He expressed the results in terms of the force required to cut through soil in relation to the rate of cutting. Figure 200 shows how the average force required for equal cutting rates decreased when the cutter was vibrated. Kondner also studied the effect of the frequency of oscillation on cutting rate, and he concluded that low frequencies were better than high frequencies. Figure 201 shows general trends observed for two shapes of cutters. Kondner's apparatus used a centrifugal driver so that the applied force could be altered by changing the unbalance of weights. The centrifugal driver thus provided a means ot applying and controlling the oscillation. Unfortunately, the natural frequency of the system of driver and cutter also influences the force actually applied to the soil. The effect of the natural frequency as resonance or a harmonic of resonance was approached probably accounts for the peaks of 2,000, 4,000 and 8,000 cycles per minute. The general trend, however, is clearly established even with the occurrence of these peaks. Cowin, Kondner, and Ayre ( 85-87 ) have published a comprehensive review of literature concerning cutting and penetrating soil. While the review sheds no light on the reasons why oscillation reduces force requirements, it does point out the need to study simple systems where variables can be easily identified and controlled. Eggenmüller (110) considered that reduction in draft may be caused by the reduction of friction along the surface of the cutting SOIL DYNAMICS IN TILLAGE AND TRACTION 281

~~(B)~~

~~< 3 er.<~~

~~3 O~~

~~10 15 20 25 30 35 TOTAL FORCE (lbs)~~

~~FIGURE 200.—Effect of oscillations in the direction of movement on the force required to cut soil. (Kondner, Waterways Experiment Station {^¿b ).)~~

~~2000 4000 6000 8000 10000 12000~~

~~FREQUENCY (CPM)~~

~~FIGURE 201.—Effect of oscillation frequency on the rate of cutting soil. (Kond- ner, Waterways Experiment Station, 1960 ( 226 ). )~~

tool As shown in figure 202, after accelerating soil in one direction a change in the direction of movement of the tool unloads the tool of soil Only the new block of soil to be cut loose by the forward 282 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~(A) (B) (C)~~

~~FIGURE 202.^Reduction in soil sliding by rapidly oscillating movement. (Eg- genmuller, Grundlagen der Landtechnik {110 ).)~~

thrust of the tool (fig. 202, B) will have to slide along the surface of the tool. Gunn and Tramontini ( 167 ) have clearly demonstrated that the total energy (draft energy plus oscillating energy) can be reduced. Figure 203 shows the total energy requirements for a rigid tool and the same tool when oscillated. Even when total

~~12 3 4 5 6 TRACTOR VELOCITY-FT/SEC.~~

FIGURE 203.—Total horsepower requirements for a tillage tool when rigid and when oscillating. (Gunn and Tramontini, Agr. Engin. {161).) energy is not reduced, a reduction of the draft energy required to pull the oscillating tool can be of advantage. The manner in which the tool can best be oscillated is therefore worthy of investigation even if the exact reason for the reduction is not presently known. Describing the path of motion is an important requirement in developing design equations for oscillating tools. The path of motion SOIL DYNAMICS IN TILLAGE AND TRACTION 283 in the earth system is relatively easy to' describe for a rotating tool, but it can be mathematically more complex for an oscillating tool. Eggenmüller (HO) reported a relatively simj)le means for describing a swinging motion superimposed on a linear motion. Figure 204 illustrates a typical oscillation in which any point on

~~PATH OF CUTTING TIP~~

~~A B~~

FIGURE 204.—A, The direction of oscillation of an inclined oscillating tillage tool; B, the path of the cutting tip. (After Eggenmüller, Grundlagen der Landtechnik {110).) the path of the tool is described by the arc of a circle. For small amplitudes, the arc can be considered to approximate a straight line. Figure 204, B shows the actual path the tip of the tool makes when amplitude, direction of oscillation, and forward speed are fixed. Eggenmüller developed mathematical equations that describe the path of motion where the oscillating motion lies in a straight line m the implement reference system. The position of a chosen point in the implement reference system, such as the tip of the tool, could be easily described at any time t if the oscillation is sinusoidal. The position of the tip at an}^ time t lies on the path of motion BD (fig. 205). The line of oscillation he is oriented in the implement reference system at the angle j) with the horizontal, and the position of the tip at any time t is given by the relationship A sin Cut where A^ o), and t are, respectively, amplitude, angular frequency of oscillation, and time. The implement reference system moves with velocity v in the earth reference system during oscillation; when the tip is at point a in the implement system, it is simultaneously at point B in the earth system. Disregarding oscillations, point a will move to point C in the earth system at time ^, and the distance B — 0 \& equal to v t. During time t the tip will have moved from a to c m the implement system, but point a in the implement reference system will have moved from B to C in the earth system. The combined motions thus result in the tip moving from B to D m the earth system. The distance B — D is the vector 284 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Y

~~IMPLEMENT REFERENCE SYSTEM~~

~~EARTH REFERENCE SYSTEM~~

FIGURE 205.—Descriptions of oscillating movements in the earth coordinate reference system. sum of the two displacements and is easily determined. If point a in the implement system is assumed to coincide with the origin of the earth system at time t — 0^ the position of the chosen point in the earth system at any time t is given hj the equations X — V t + Ä cos ip sin 0) t^ (148) y — — J. sin (/) sin (út. (149) A plot of X and y values from equations 148 and 149 will produce a periodic curve of the form shown in figure 204, B where each chosen point x^y corresponds to a point on the path of the tip of the tool. Equations 148 and 149, therefore, represent the means for determining the path of motion of a point subjected to sinusoidal oscillations constrained along a straight line and superimposed on a path of linear motion. The parameters of the path of motion equations are v^ Ä^ (f) and ca, and they should be the variables that appear in any design equations. Eggenmüller used an experimental apparatus that produced the type of oscillation indicated in figure 204, A to measure the inñuence of the path of motion parameters identified in equations 148 and 149. He used soil in an indoor soil bin, which he described as a fine sandy loam with an average moisture content of 16 percent and an average porosity of 48 percent. A fixed cutting angle (6 in fig. 204, A) of 20° and a working depth of 9 centimeters was maintained for all studies. Figure 206 summarizes experimental results indicating the influence of various oscillation parameters on draft. The draft of the oscillating tool is expressed as a percentage of that of the same tool operated without oscillations; therefore, all of the experimental treatments shown are directly comparable. The data indicate that oscillation decreased draft in every instance SOIL DYNAMICS IN TILLAGE AND TRACTION 285

~~6 9 12 .4 .6 .8 AMPLITUDE (mm) DIRECTION OF SPEED Vo(m/8) OSCILLATION (*»)~~

~~FIGURE 206.—Effect of oscillation parameters on the draft of an inclined tillage tool. (Eggenmüller, Grundlagen der Landtechnik {110).)~~

—often more than 50 percent. Over the ranges of values of parameters studied, amplitude had little effect after it exceeded 6 milh- meters whereas changes in the direction of oscillation gradually decreased draft as the direction was increased from 0 to 30 degrees. In every instance, draft was reduced as frequency of oscillation was increased. Frequency had the largest effect in reducing draft and forward speed the least, whereas amplitude needed only to exceed a certain threshold value of approximately 6 millimeters. These conclusions should be applied to other soil-tool systems with caution, since only one soil condition was mvestigated. iS^ever- theless, this work demonstrates the principle of identifying^ experimental variables for design equations from the parameters of mathematical equations that describe path of motion. If similar results can be obtained in other soil conditions, it may be possible to develop general equations to express the relations shown m figure 206. Eggenmüller measured the power required for oscillating the experimental tools and qualitatively assessed the final condition ot the tilled soil. Since power was measured in the form of the electrical input to an inefficient motor that was used to drive the oscillating mechanism, the energy measurements must be considered only as trends. The direction of oscillation and working depth had little effect on the oscillation power requirement. Increasing the amplitude increased power requirements, and doubling the frequency ot oscillation nearly doubled power requirements. From these experiments Eggenmüller concluded that low amplitudes and frequencies 286 AGFICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE would be most practical. Power reductions due to draft reductions were increasingly offset by increases in oscillation power requirements. With regard to the final soil conditions, Eggenmüller concluded that the oscillating tool produced somewhat smaller clod sizes and appeared to turn the clods over rather than allowing them to fall back into their original position. No quantitative measurements were made, but difference between clods produced by rigid and by oscillating tools could be detected visually. Shkurenko ( 386 ) studied the effect of oscillation on the draft of a blade. He used a simple system where controlled oscillation and linear motions were possible. Shkurenko conducted his experiments in one soil condition, which he described as a compact clay with a moisture content of 26 percent. The blade was a thin metal plate that had the leading or cutting edge sharpened. The plate was positioned in one test so that the plane in which the blade was situated was vertical and contained the direction of travel. This orientation is designated parallel to the direction of travel. In another test the blade was positioned so that the cutting edge was perpendicular to the direction of travel. The plane of the blade was maintained at an angle of 45° with the horizontal plane to simulate a simple inclined-plane tillage tool. This orientation is designated perpendicular to the direction of travel. Two directions of sinusoidal oscillation were used; they are designated as vertical and horizontal. These directions constitute values for <¡) of 90° and 0°, respectively (fig. 205). Eclations were established between the reduction in draft force and the amplitude of oscillation for the limited experimental conditions. The relation had the form Ô = yAO''\ (150) where 8 = ^^^^^ (non-oscillated) - draft (oscillated) draft (non-oscillated) A — amplitude of oscillation, 7 = a constant of proportionality depending on the frequency and direction of oscillation, depth and angle of cutting, and soil properties. Table 32 lists evaluations of y (cm)-o83 that were determined for various specific operating conditions. The influence of the oscillation of the blade was 1.6 times greater when applied in the horizontal direction than when applied in the vertical direction. Shkurenko also obtained a relation between the change in draft and a quantity he termed oscillating speed. The quantity was proportional to the frequency of oscillation and speeds of 140 to 170 centimeters per second were required to reduce draft from 50 to 60 percent. This trend of increasing speed of oscillation to decreasing draft substantiates Eggenmüller's data. Figure 207 shows the effect of forward speed on the draft of an oscillating and rigid tool. For the conditions studied, forward speed did not have a large effect on draft, since a sixfold decrease in speed produced only a 25-percent decrease in draft. Dubrovskii ( 107 ) and others have studied other aspects of oscillating tools. Dubrovskii reported that the length of the oscillating SOIL DYNAMICS IN TILLAGE AND TRACTION 287

~~RIGID ^ 800 O o - 600 OSCILLATED < 400 (r Q 200~~

~~0.4 0.8 1.2 1.6 2.0 VELOCITY (M/S)~~

FIGURE 207.—Effect of forward speed on the draft of oscillating and non- oscillating (rigid) tillage tools. (Shkurenko {386).) motion was increased by increasing velocity, so that larger sections of soil were broken loose. Hendrick and Buchele ( 180 ) reported that the reduction in draft of an inclined-plane tillage tool was rapid until the frequency of oscillation approached the frequency ot the formation of shear surfaces. When Garbotz and Drees {1J8) vibrated a bulldozer blade, the force required to move the blade was reduced. An eccentric weight rigidly attached to the blade was rotated to cause the blade to vibrate. The actual path of motion was not controlled since it would vary, depending on the torces acting at any instant of time. Nevertheless, draft was I'.educed. Practical difRculties are encountered when massive tools are vibrated, but Eggenmüller ( 111 ) succeeded in vibrating segments ot a moldboard plow. . ^ .^^ . ..^ , . Thus, considerable evidence exists that oscillating a tillage tool can increase the effectiveness of the tool—for example, it reduces draft and increases soil breakup. But little information has been accumulated to explain how and why an oscillating tool is more effective than a rigid tool. Although design equations can be empirically developed for oscillating tools, so many types of oscillation

TABLE m,—Effect of the direction and frequency of oscillations on the coefficient for a simple Hade operating at a speed of 0.3 meter per second Direction of Orientation of Oscillating oscillation blade frequency Vertical Horizontal c./s. 7(cm)-ö.83 7(cm)-ö.83 Perpendicular to direction of travel and inclined at 45° from the horizontal _ - -- 100 0.42 0.60 210 .75 1.19 Parallel to direction of travel and vertically inclined _ _ _ - 100 .38 .59 210 .70 1.10

SOURCE : Shkurenko {S86). 288 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE are possible that basic studies will eventually be needed to properly evaluate the principle. Most modes of oscillation studied have been sinusoidal, but many additional types may be used. Hence, the possibility of optimizing the effect of oscillating a tillage tool by empirical observation seems doubtful until knowledge that explains why oscillation is effective becomes available. For example, Eggen- müller's direction of oscillation of 0° moved the tool forward and backward through the soil without any up or down movement. One might consider that this is no different from a rigid tool except that the speed of forward movement is much greater. But such is not so, since higher forward speeds require higher drafts for a rigid tool. The reduction in draft observed for oscillating tools must have its origin from some action such as the reduction of friction or the coincidence of movements and shear failures. Probably new behavior equations concerning oscillating forces will be required to explain the phenomenon. Until the reason for response to oscillation IS established, the design of oscillating tools must be largely inventive. 5.6 Implements Individual tillage tools cause soil reactions that extend a finite distance beyond the edge of the tool (fig. 142). If two tools are simultaneously operated sufficiently far from each other, the tools can be considered to be operating independently. When the two tools are brought close to each other, however, they begin to influence each other. Design equations available for a tool can be used only when a tool acts independently. When two tools begin to interact, the interaction cannot be represented by design equations developed for individual tools. The interactions must be recognized and quantitatively described in order to be incorporated into design. Fortunately, interactions often can be utilized to control or to better effect the desired type of soil manipulation. Interactions also frequently reduce the forces required to move the combined system of tools through the soil. Optimizing all effects of an interaction, therefore, becomes a major challenge to the tillage tool designer. To provide quantitative information that designers can use to develop proper designs is the challenge for the researcher. Pre- sumably, the interaction can be quantitatively described with behavior equations that are combined to form a mechanics. The solution of the system of equations will inherently include a description of the interaction. For example, incorporating two tools into the mechanics involves not only specifying the nature and action of the two tools but also specifying their position with respect to each other. The position description can be general since it contains parameters. If a general solution of the mechanics can be obtained, the resulting design equations can be used to optimize the effect of the interaction. In the derived approach, developing a quantitative description of the interaction is the only further step required, and it involves no new principles. The development of a quantitative description of interactions for use in empirical design equations can be undertaken in several ways, abstract design factor in equations 132 and 133. As such, initial For example, the interaction may be viewed as a fourth controlling SOIL DYNAMICS IN TILLAGE AND TRACTION 289 soil condition Si, shape Ts, manner of movement Tm, and interaction / would be the independent design factors. On the other hand, the two or more individual tools may be considered to be one new shape, and the interaction can be incorporated into the shape description. It is also possible to describe the interaction as a modifier of the design equations applicable to an individual tool. Finally, the interaction may be considered to be a variation in the manner of movement of the tool. While each approach is plausible, none seems to be particularly superior to any other when all combinations of individual tools are considered. Probably, one approach will be preferred for certain circumstances. Any one or all of the approaches may, therefore, be used in developing design equations by empirical methods. Implement design as considered here is concerned with the interaction between a group of two or more tools and the soil. Struc- tural arrangements and limitations are important, and in some instances they may override the possibility of utilizing interaction. Nevertheless, only the interaction, so far as it affects soil manipulation and tool forces, is considered here. The location of individual rotary tiller tines about the axis of rotation produces a different effect from the simultaneous interaction now being discussed. In the rotary tiller, a change in the location of a tine changes the boundary condition for a subsequent tine. Tines can be spaced far enough apart so that they do not pass simultaneously through the soil and interact. The boundary condition created by one tool, however, may greatly inñuence the action of a tool that operates in the same vicinity at a later time. Interaction as used here refers to the simultaneous operation of tools near each other. Both simultaneous

~~TABLE Z3.—Effect of the type of coulter on the draft of a ploio-coulter combination~~

Draft force Soil tvDe and Operating moisture content speed Disk-jointeri Coulter-jointer M.p.h. Pounds Pounds Norfolk sand : ñ 6 Deroent 3.0 203 369 7 5 Deroent 3.0 214 241 9 0 Deroent 3.0 311 332 ñ 6 nercent 4.5 350 417 7 ,5 nercent 4.5 268 283 9 0 nercent 4.5 311 401 Hiwassee sandy loam : 8 0 Dercent 3.0 504 562 9 7 Dercent 3.0 501 608 8 0 nercent 4.5 560 663 9 7 Dercent 4.5 559 687 Decatur clay: 13 7 Dercent 3.0 675 824 16.1 percent 3.0 875 938 Average 444 571 iThe disk jointer was a 17-inch concave disk operated 10°-12° from the direction of travel. Both coulters were operated 31/2 inches deep, with the plow cutting a furrow 14 inches wide and 7 inches deep. 290 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE interactions and boundary condition interactions must be considered in implement design. Interactions can occur between tools of different types that are part of the same tillage implement. The draft of a plow and coulter combination varies as the position of the coulter relative to that of the plow varies. Because of the interaction, the draft of the plow and coulter combination may differ from the sum of the two components measured separately. This effect has been demonstrated by experiments in which different types of coulters were used. Table 33 compares the implement draft of a moldboard plow used in conjunction with two types of coulters. Berry ( 39 ) found that use of a disk jointer reduced total implement draft. Apparently, the disk jointer created a condition so that the combination of tools reduced total draft force an average of 15 percent. The extent to which this reduction in draft is desirable depends on the comparative covering characteristics of the two tool systems. When the performances are equal, there may be an economic basis on which to select the disk coulter. The interaction in a double-cut plow is more apparent. Figure

(B) FIGURE 208.—A, A double-cut plow ; B, the tillage action of a double-cut plow. (Domsch, V.E.B. Deutscher Landwirtschaftsverlag, Berlin {lOJ^).) SOIL DYNAMICS IN TILLAGE AND TRACTION 291 208 indicates the principle of a double-cut plow that was designed to break up a dense layer below the normal plowing depth. The double-cut plow is also useful when infertile or wet material should be kept separate from the surface soil. Figure 208 B shows how the lower share may loosen and pulverize the soil but leave it in the furrow bottom without any appreciable mixing with the surface layer. Notice that the lower cut moves soil upward into an unconfined area. As a result, the same volume of soil can be tilled in layers with less energy than is required to till it in a single cut. Table 34 shows how draft force is reduced by using the double-cut principle {357), The same volume of soil was tilled by the two types of plows; however, the double-cut plow required 25 to 30 percent less draft force than the conventional plow. Notice also that the various depth settings of the double-cut plow produced different total drafts for the combination. While the interaction appears to be small, the effect can be truly evaluated only when each portion of the double-cut plow is measured simultaneously.

~~TABLE 34.—Comparison of conventional and double-cut plows loith respect to the draft force required to ploio a furrow H inches ivide to several depths~~

~~Depth of operation Draft force~~

Type of Double-cut Conventional Conventional plow2 soil moldboard moldboard Double-cut Main Lower plowi plow2 plowi share share Inches Inches Inches Pounds Pounds 8 5 3 335 235 Norfolk 10 6 2 335 270 sandy 10 6 4 473 356 10 6 4 473 350 Hiwassee 8 5 3 653 513 sandy loam 8 6 2 653 520 1 standard 14-inch moldboard plow. 2 The double-cut plow was similar to the one shown in figure 202. The main plow was a 12-inch moldboard that was symmetrical with the 14-inch plow, but it was equipped with two 10-inch shares. SOURCE : Reed and Berry {351 ).

How much of the reduction in draft of the double-cut plow, as compared with the conventional plow, was the result of optimizing the tool interaction (the two shares) was not determined. The overall dimensions of the double-cut plow were smaller than those of the conventional plow. Thus, the sphere of influence of the double-cut plow was utilized in breaking out rather than cutting the soil. When tearing or shearing force is less than cutting force, draft should decrease. One additional consideration is that the two plows probably performed different amounts of work on the soil. If both were satisfactory, the double-cut plow would have an economic advantage. Another aspect of the interaction concerns the amount of soil disturbed by individual tools on an implement. In section 4.5.5, the effect of straight tines was discussed and figure 142 illustrates the 292 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE effect. Thompson and Kemp ( Í29 ) have developed a graphical procedure that provides a rapid and precise means for determining disk spacing and depth of operation in order to best utilize the capabilities of disks (fig. 209).

~~(A)~~

~~(B)~~

~~(C)~~

~~FIGURE 209.—Graphic analysis of disk cuts. (Thompson and Kemp, Agr. Engin. ( Jt29 ).)~~

In figure 209, J., B^ and 0 illustrate the effect of changing the distance between two adjacent disks on the area of soil cut when the disk is oriented at an angle of 45° with the direction of travel; Z>, E^ and F show the effect on the area of soil cut as the angle of a gang of disks with a fixed disk spacing increases from 30° to 60°. The aspect of interaction covered by the method is the changing of boundary conditions. The possibility that adjacent disks may influence each other because of simultaneous operation has to be evaluated by other means. One of the best studies of interaction, reported in the U.S.S.E. ( 515 ), concerned teeth on a cutting blade. A common example of this kind of tool is a dragline scoop. Some of the research efforts in the U.S.S.E. were directed toward evaluating the scoop, but others used simple experimental tools to study the interaction. Figure 210 shows an experimental arrangement where a single tooth was fitted on a cutting blade. Three widths of teeth each 5 centimeters long were studied (table 35). The area of the soil slice cut off by the tool is the product of width of cut {Wc) (fig. 210) and depth of cut. The work expended is proportional to the force required to move the blade, and data indicate that the narrow tooth required the least force. On a work-to-area basis, the narrow tooth was only 70 percent of the wide tooth—a 30-percent increase SOIL DYNAMICS IN TILLAGE AND TRACTION 293

FIGURE 210.—An experimental cutting blade with a tooth. (After Zelenin ( 515 ).) in the effectiveness of the cutting blade. The results of the soil manipulation can be expressed by the area of soil cut loose, so that the work-area ratio simultaneously considers both design equations. These data clearly indicate an interaction between the tooth and cutting blade. Zelenin ( 615 ) also studied teeth on an experimental dragline scoop. The scoop had a volume of 0.38 cubic meter and was operated at various angles of inclination to the horizontal. Figure 211 shows the shape of the teeth and the parameters that define the shape of the teeth. The depth of the cutting blade was kept constant for the scoop but the teeth on the blade were extended below the cutting blade a distance X, as shown in figure 211, A, The teeth used were simple wedges with an angle of sharpness, ß,

~~(A) (B)~~

FIGURE 211.—A, Parameters describing the shape and orientation of teeth attached to a cutting blade; B, parameters describing the width and spacing of teeth on a cutting blade. (Zelenin ( 515 ).) 294 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE of 16° and a width of 15 millimeters. The scoop was operated in clay and loam soils. Teeth reduced draft force, (table 36). The reduction occurred even though the teeth actually operated somewhat deeper; they added a distance X to the cutting depth. Thus, teeth clearly decreased the force required to move the scoop through soil.

~~TABLE 35.—Effect of the width of teeth on the work required to cut a path of soil~~

Width of Width of Area of Ratio : teeth cut Depth of Work cut expended soil work/ slice area Centi- Centi- Centi- meters meters meters Kg.-m. Sq.dm. 3 10 16.1 8.35 1.61 5.18 7 10 17.0 11.52 1.70 6.70 10 10 16.5 12.22 1.65 7.40 SOURCE: Zelenin { 515 ).

~~TABLE 36.—Effect on the draft force required to cut soil hy model dragline scoops equipped with teeth~~

Lift angle of scoop Tool Depth of cut 7° 18° 42° Centimeters Kilograms Kilograms Kilograms Scoop (no teeth) 10 420 420 535 Scoop (with teeth) 10 315 328 400 Percent Percent Percent Saving in draft force 25 22 25 SOURCE : Zelenin {515 ).

The spacing and width of teeth along the cutting blade were also investigated by Zelenin. In a series of experimental arrangements, the ratio h/a shown in figure 211, B was varied. The results are shown in figure 212. The data indicate that a definite minimum occurs at a h/a ratio of approximately 2.5. The curve is based on a limited number of points, however, so that the exact magnitude of values may be questioned. Since a ratio of zero indicates an infinite number of teeth and a ratio of infinity indicates no teeth, the data do not appear too unreasonable in light of the data included in table 35. An interaction between teeth on a cutting blade is clearly demonstrated by these data. Length of teeth on cutting blades was also investigated by Zelenin. For a given orientation (angle of cutting a in fig. 211, Ä), an increase in tooth length results in a greater clearance distance X below the cutting blade. Added length was detrimental because it decreased the strength of the tooth, increased resistance to cutting, and increased "littering" (some of the loosened soil slipped between the SOIL DYNAMICS IN TILLAGE AND TRACTION 295 1.0 ■

~~X X h- K UJ U UJ LU 1- h- X O § 1 0.8 UJ LÜ (y fy Q Q ü- U.~~

~~O O 2 Z h- H h- t Z5 3 Ü O 0.6~~

~~FIGURE 212.—The relation between spacing-to-width ratio of teeth on a cutting blade and draft of the blade. (Zelenin ( 515 ).)~~

teeth and was not placed in the scoop). Based on these premises an equation of the form X = L sin {y^i} (151) where X — clearance distance, L — tooth length, y — cutting clearance, ß = angle of sharpness of tooth, expressed relations that affected a suitable design. Based on experience, Zelenin reported that the optimum cutting angle a should be about 20° for most conditions. A maximum angle of sharpness is thereby specified, since a minimum cutting clearance angle of 5° is considered essential. An angle of cutting of 30° was considered to be maximum, so that a compromise between strength (large angle of sharpness) and lowest draft (20° angle of cutting) has to be effected. A final point may be made about tillage implements. Figure 213 shows an example of a drawn tool whose action is modified by the dynamic action of a power-driven rotor. Endless possibilities exist for developing multipowered implements, particularly since engine power ceases to be a limiting factor. Interactions between complex tool systems of this type are essentially unexplored. 5.7 Principles of Force Application To design, by definition, is to conceive a scheme or plan. Since design implies intent, it becomes important to judiciously choose 296 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~FiGUKE 213.—Combination drawn and rotating tillage implement. (Davidson and Collins, Agr. Engin. (94 ).)~~

and vary design factors in order to obtain the best possible design. Two tillage equations described in section 5.2 can be used in developing optimum designs or in determining the influence of various design factors on performance. Nothing about the factors to be selected can be determined from these equations. As a result, it becomes necessary to choose design factors which, by experience or intuition, seem to be of basic importance and study them. It is within the scope of soil dynamics research to provide information that will ultimately assist in identifying and selecting design factors. At present (1965), little information is available; however, the general nature of information that will be required can be foreseen. To have the skill necessary to design tillage tools that will operate in the most efficient and most effective manner, the basic principles of the tillage actions must be identified, developed into distinct concepts, and properly used. These principles should be used as a guide to direct the application of forces and movements of tools in order to achieve the desired soil conditions. Following are illustrations of several basic principles of force application: 1. Forces should be applied to the soil in the direction that requires the minimum force to cause the desired action. When only a cutting action is desired a flat blade can be used to cut the soil without applying force to lift and loosen it. 2. The mechanical rigidity of the soil mass should be used as a holding body. The application of force in the desired location and SOIL DYNAMICS IN TILLAGE AND TRACTION 297 direction can be controlled when the soil is rigidly held. The direct fragmentation to the desired clod size may be better achieved by using the inherent strength of the undisturbed soil mass as a holding body than by disrupting the mass and then reducing the size of granules by repeated operations. . 3. The soil-tool geometry should be designed so that the confining action of the soil is either minimized or utilized in conjunction with the direction of force application of the tool. Small cuts may reduce the total force on a tool due to reduced soil confinement or due to the lesser weight of soil on the tool. The removal of soil from the cutting areas of augers, ditchers, etc., prevents binding and the need to displace soil against a high mechanical resistance. The direction of force may be controlled to utilize the confining action of the soil mass. In packing or crushing operations with rollers, a large- diameter roller traps surface clods more successfully than a small- diameter roller, which tends to roll them in front of the roller. 4. The rate at which force is applied should be controlled. Im- pact forces may be applied to detached soil fragments in order to exploit soil inertia and build up stresses in the fragments. Brittle clods may be broken without entrapment and confinement by the soil mass. 5. The sphere of influence of an application of force should be controlled. Changes in strength caused by strain hardening resulting from soil compaction may be undesirable or they may influence the reaction of the soil to subsequent tillage actions. Extraneous forces such as those imposed by secondary forces—that is, subsequent machine operations—frequently undo the work done on the soil by primary tillage forces. The size and shape of tools also govern the sphere of influence of the tool. 6. The force applications should be directed to control the size and shape of detached soil blocks. The shape and path of movement of the tool may be used to influence the size and possibly the stability of soil blocks. 7. Balanced force applications should be used for multiple tool units. The controlled movement of several tools can insure order and regularity in the action of the tool on the soil and result in a more uniform and efficient use of the power input. 8. A sequence of forces should be applied to execute complex actions. The use of a coulter preceding a plow cuts plant material and establishes order in a randomly spread plant material so that effective covering can be accomplished by the plow. 9. The time of force applications in a system should be controlled. Breaking clods immediately after plowing will preclude the development of high strength by drying before breakdown is effected. Waiting for drying, on the other hand, increases strength so that compaction is resisted. There should be a continued search for other principles since they provide a sound basis not only for the design of tillage tools but also for the subsequent development of methods by which they should be used. The development and use of principles for design will permit a more direct and accurate selection of design factors for study in the design equations. Unless this is done, pertinent factors may not be introduced as quickly as possible. 6. PERFORMANCE OF TILLAGE TOOLS

6.1 Introduction Design was discussed in chapter 5 without regard to use of tillage tools. Disregarding application was convenient because it simplified the study of design. Application cannot always be ignored, because the ultimate purpose of design is not to build tools but to change undesired soil conditions into new soil conditions that will better serve some specific intended use for the soil. Performance is defined by Webster as the act of performing. To perform is to accomplish, or to carry on to the finish. Performing implies action; and performance can have almost as many specific meanings as there are specific actions. In tillage, the obvious action is the manipulation of the soil into a different condition. Perform- ance of a tillage tool thus may be defined as the production of a change in soil conditions by manipulation of the soil. Performance includes two distinct and separate factors of interest : the amount of soil manipulation, and the magnitude of forces required to cause the manipulation. These factors must be quantitatively assessed in order to measure tillage tool performance. Each factor of tillage tool performance is fixed, since it does not vary for a fixed manipulation. As indicated by tillage equations 132 and 133, in chapter 5, the use of a given tool in a given soil condition results in a fixed change in soil condition. The difference between the initial soil condition Si and the final soil condition Sf is a measure of soil manipulation. Similarly, the forces required to cause the manipulation do not vary for a fixed manipulation. Given the necessary information and the idealized type of complete mechanics discussed in chapter 4, tillage performance could be calculated. Similarly, if the tillage equations were fully developed, they could be used to calculate performance. Tillage performance, when defined in this sense, is a fixed and determinable entity that can be used to express the performance of a soil-tool system. Performance embraces more than just changing the soil to a new condition. First, the tillage tool should perform efficiently ; that is, soil conditions should be altered with the smallest expenditure of energy required to operate the tool. Second, the final soil condition must be acceptable. A tillage tool may manipulate soil very efficiently, but the soil condition it produces may not be suitable for the intended use of the soil. Performance, in terms of suitability of soil conditions, must be evaluated by comparing the final soil conditions that are produced with those that are desired. Perform- ance, in terms of forces, must be evaluated by comparing forces required for manipulation with available or acceptable forces. The soil conditions that are to be produced by tillage must be expressed in criteria that characterize the soil in terms associated 298 SOIL DYNAMICS IN TILLAGE AND TRACTION 299 with its intended use. These criteria are specifically determined by the intended use for the soil and not by anything intrinsic m a tillage tool or even the soil itself. The physical condition or state of soil determines the degree to which it may be utilized for a specific purpose. The term soil conditions, as used here, includes all physical characteristics of the soil that may be pertinent to its use. Soil in a specific condition may be suitable for one intended use but not another. The difference here is not in the condition of the soil but in the requirement that must be met by the soil for each intended use. Evaluation is a measure, or an estimate if quantitative descriptions are not used, of how close the actual performance is to the intended performance. Evaluating the performance of tillage tools requires broadening the scope of interest to include the purpose of tillage. This broadening of the scope of interest completes the cycle of interests encompassed in soil dynamics. The need for soil dynamics comes from the need to understand how to manipulate soil. The types of manipulation that are required are determined by the intended use of the soil. In the development of soil dynamics, interest was first vested in the dynamic properties of soil as defined by soil behavior equations. This interest stems from the fact that the soil is placed in motion during a manipulation and its dynamic behavior becomes of importance. The soil behavior equations are basic to a soil-tool mechanics; mechanics is basic to design; and design is basic to performance. Evaluation of performance takes into consideration the intended use of the soil as well as the performance of a tool, and the scope of interest of soil dynamics is completed. Evaluation of performance requires (1) measures of soil conditions to determine when and how much a condition is changed by a manipulation and (2) measures of the forces required to cause the manipulation. Generally, soil conditions cannot be controlled without tillage, so that all changes must come from the use of a tool. To change the performance of a tool, there must be a change in its shape, manner of movement, or constructional material. Changes of this type are effected by the design of a tillage tool. Obviously, the designer must consider evaluation of performance so that there can be an interplay of design, performance, and evaluation. Because of the need for this interplay and because of the complexity of the various factors involved, quantitative description is required for each of these factors. With quantitative descriptions of design, performance, and evaluation, mathematical principles can be employed. Quantitative descriptions of performance are difhcult because no method has been developed for describing soil conditions adequately. Tool forces can be readily measured and reported in representative terms, so that the force aspect of performance is relatively easy to describe. Mathematical representations of force systems are well developed. Quantitative descriptions of soil conditions, on the other hand, are not well developed. In fact, at present (1965), specific conditions usually cannot be quantitatively described with regard to the intended use of the soil. Some of the problems of describing soil conditions with respect to tillage tool performance are discussed in section 6.2. 300 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE In retrospect, we can see how inability to characterize both actual and desired performance has hampered the evaluation of performance and has influenced the design of tillage tools. Lack of quantitative descriptions of soil conditions precludes establishing an accurate performance goal for a particular tool. As a result, in seedbed preparation, that portion of the required soil manipulation not accomplished by a moldboard plow, for example, is completed by subsequent harrowing, levelling, or packing. Without a specific performance goal, the inadequacies of the moldboard plow go un- noticed and are compensated by additional tillage operations. The development of methods by which to describe performance of tillage tools and to evaluate performance in quantitative terms will materially improve the means available to better design tillage tools. 6.2 Description of Soil Conditions A description of soil conditions that can be successfully used within the framework of soil dynamics must meet two criteria. First, the description must be quantitative and, second, it must be easily interpreted in terms associated with the behavior implied in the intended use of the soil. For example, electricity is known to flow in accordance with Ohm's Law, If a soil is to be used as a ground return in an electrical circuit, a description of the soil condition should specify the electrical resistance of the soil. This is the only means by which the soil condition can be interpreted in terms compatible with Ohm's Law. If the condition is not described by resistance but by specifying the percentage of clay in the soil, its moisture content, porosity, temperature, and similar factors, the description cannot be interpreted in terms of resistance and hence has limited value. Thus, while the material and static state descriptions of soil may be quantitative, they do not reflect the role of the soil in the behavior of interest and the descriptive parameters are not compatible with the requirements of the behavior equation (Ohm's Law). To be compatible, a description of soil conditions must physically represent the parameters inherent in a behavior equation that reflects the behavior of soil in its intended use. Soil to be used for some specific purpose is subjected to a force system. Whenever soil is placed in use, the soil acts ; the applied forces cause the action. For example, in constructing roads, dams, or building foundations, mechanical forces are applied to the soil ; the soil is expected to resist. The mechanical resistance is the soil action, since the soil is not just occupying space and doing nothing. In tillage, the soil is also subjected to mechanical forces, but it is expected to fail and yield. The movement of the soil is the action. When electricity is transmitted through soil, electricity applies force to the soil; when the soil is used as a medium for plant growth, air, water, and plant roots apply forces to the soil. All of these examples illustrate the fact that whenever man uses the soil for some purpose, the soil is subjected to forces. As discussed in section 3.1 and illustrated in figure 39, the soil responds to applied forces in one of two distinct reactions. The soil may resist and enter into a passive behavior relation, or it may yield and enter into an active behavior relation. These reactions are theo- SOIL DYNAMICS IN TILLAGE AND TRACTION 301 retical but are separate and distinct. That the reactions can and often do occur simultaneously does not negate the principle of their independence; it merely complicates the situation. The important point, however, is that any use of soil involves either an active or a passive behavior of the soil. These behaviors can be represented by suitable behavior equations. As was discussed in section 3.1, the equations contain parameters and the parameters provide a means for numerically describing the role of the soil in the behavior. Since the parameters are defined by a behavior equation that represents the specific behavior associated with some intended use, behavior parameters provide the mechanism by which to describe soil conditions in terms that are compatible with the intended use. Examples of active behavior equations and various means for assessing the parameters were given in chapters 2 and 3. Active soil behavior is relatively easy to visualize because the soil itself actively participates in the behavior. This active participation is the movement and yield of the soil. Passive soil behavior is distinctly different from active behavior. In spite of this distinct difference, the parameters of the equations that represent the respective behaviors serve the same function, namely, they assess the role the soil plays in each respective behavior. j, r\^ j To visualize passive behavior, consider the application of Ohms Law to soil. In this application, the soil acts as a "conduit"^ or a "conductor" for the now of electrons; it serves as a transmitting medium. During this behavior, the soil itself is not active ; that is, it is not moving. Eather, by its rigidity it is guiding and controlling the active material, the electrons. Also when air or water moves through soil, the soil without motion guides or controls the flow of the active material. Thus, in passive soil behavior the transmitted material is the active material, whereas in active soil behavior the soil itself is the active material. Furthermore, passive behavior of soil always involves two materials—the soil and the material being transmitted. These two materials may be envisioned to be a combined system, and an overall behavior equation will represent the behavior of the system. This same type of relation applies to the soil-tool system where the soil is the active material and the tool guides and controls the flow of soil. The functional relation provided by equation 132 (discussed in ch. 5) thus might serve as a passive behavior equation of a tillage tool. It is important to separate soil behavior into active and passive reactions. Theoretically no conflict exists, since the separation is a mental model of the physical behavior; in practice conflict does exist, however, because active and passive reactions can and do occur simultaneously. Furthermore, force systems can and do vary continuously in magnitude. Whether the same force system causes the soil to enter into a passive or an active reaction depends on the magnitude of the forces. In other words, there is no way to look at forces and separate them into those that will cause passive behavior and those that will cause active behavior. In practice, however, a separation can be made. To illustrate, consider water flowing through a pipe. Characteristics of the pipe such as size, shape, length, and roughness guide and control the flow of the water through the pipe—that is, they determine the role of the pipe m the 302 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE pipe-water system. In this role, the pipe enters into a passive behavior relation. Actually, the pipe itself is subjected to the pressure forces of the water and the pipe material enters into an active behavior relation. From a practical standpoint, the active relation can be ignored as long as the pipe is strong enough to withstand the pressure. Stress-strain and yield equations are the active behavior equations of the pipe. If the water pressure is large enough, the pipe will fail and in a sense be ''"manipulated." Somewhat the same separation of reactions can be visualized for soil. One big difference, of course, is that soil is a three-dimensional semi-infinite material whereas a pipe contains a finite amount of material. This difference complicates the separation of the reactions for soil but does not negate the principles of similarity. Thus, from a practical standpoint, soil behavior can be separated into two reactions. In tillage, we are usually interested in only one behavior at a time and the other can be ignored. Two problems are associated with selecting and using soil behavior equations to describe soil conditions. First, soil conditions are not constant with time. In other words, soil conditions can change even though tillage forces are not being applied. Changes are caused by forces so ill defined that they are generally called weathering, wetting, or drying. In tillage, we are primarily interested in the immediate effect of tillage on soil conditions. Tillage cannot control soil conditions after tillage has been completed. Since a tillage operation is usually completed m a very short time when compared to forces involved m weathering, soil conditions before and after tillage are essentially constant. Therefore, with regard to tillage performance and its evaluation, changes m soil conditions that are associated with time can be ignored. Changes associated with time are separate and independent of tillage and may be studied by themselves. Ultimately, of course, m a system of wider scope, the effect of both tillage and time on soil conditions must be considered. Kepeated determinations of the parameters of the behavior equations provide the means by which to follow changes in soil conditions regardless of the applied forces. The second problem is the selection of behavior equations that are compatible with the intended use of a soil. Obviously, only behaviors that are involved with the intended use are of interest and other behaviors can be ignored. Some soil behavior equations are not directly related to the intended use. A direct relation always exists if the inputs or outputs of the behavior equations are directly related to the intended use. For example, a direct relation exists*^ in traction, in support for a footing, or m an electric ground return. The forces involved in active behavior are precisely those that provide traction or support a footing. The amount of electricity transmitted is of direct concern when the soil is used as a ground return. An indirect relation always exists if the soil behavior equation represents only a subsystem of an overall system of interest. An indirect relation exists when complete control of the overall system is not totally vested in a soil condition and particularly a soil con- SOIL DYNAMICS IN TILLAGE AND TRACTION 303 dition created by tillage. One complex system of interest involves the influence of tillage on the growth of plants. At least four systems are interrelated in tillage and plant growth. These are the soil-machine, soil-water, soil-air, and soil-plant systems. Plant growth itself is a form of biological behavior that depends on the environment of the surrounding atmosphere as well as of the soil. The oxygen and water required by a plant is determined by the plant but may be influenced by the ambient environmental conditions. Only the soil conditions are affected by tillage, and these conditions control the rate at which oxygen and water are transmitted through the soil to the plant roots. Consequently, the only behavior associated with the soil-machine system is the production of different soil conditions. These different soil conditions control the movement of oxygen and water—that is, the soil-air and soil- water systems. The availability of oxygen and water influences but does not control plant growth. Thus, plant behavior cannot be directly related to the type of tillage tool or even to forces applied to the soil by the tillage tool because of the influence of intervening systems. Performance of the soil-plant system must be separated from the soil-machine system. Thus, while in plant growth the growth is of interest, this behavior is neither directly related to the soil nor controlled by it. Soil conditions must be described in terms that are directly related to the soil, namely, the transmission rates of oxygen and water, rather than in terms that are directly related to plant growth, the behavior of interest. Thus, selecting behavior equations to describe soil conditions is not always simple or easily achieved. Lack of simplicity, however, does not negate their usefulness in describing soil conditions. In principle, the establishment of quantitative descriptions of soil conditions by using soil behavior equations is simple; in practice, however, it is complex. The complexity results primarily from lack of identified behavior equations. Passive soil behavior equations are few. They have not been developed for various reasons. First, there have been no concentrated efforts to establish passive behavior equations. Second, there has been a failure to separate situations where soil has direct control of the intended use from situations where soil has indirect influence. Unless this distinction is made, there will be little progress toward developing adequate behavior equations. In a direct relation such as traction, soil conditions control the performance of a specific device. In an indirect relation such as plant growth, soil conditions do not control; they only influence. Indirect relations do not provide a one-to-one correspondence rule between soil conditions and use; therefore, quantitative relations cannot be established. A third reason why development of passive behavior equations, in particular, has lagged is that soil conditions change with time. Internal movements due to the application of forces that cause swelling and shrinking change soil conditions. Changes of this type make the development of passive behavior equations very difficult. The method by which soil conditions can be described in terms of the intended use is clear, but it cannot presently be implemented because the necessary behavior equations are not available. 304 AGRICULTURE HANDBOOK 31G, U.S. DEPT. OF AGRICULTURE Meaningful descriptions of soil conditions and, hence, of tillage performance hinge on the establishment of soil behavior equations. Once established, however, the parameters of the equations must be assessed. One means of assessing the parameters is by direct measurement. While straightforward, this means has one serious limitation. The limitation is not that a measurement must be made, but that a different measurement is required for each behavior equation. An assessment of soil from which all behavior parameters could be determined is desirable. Intuitively, we know such an assessment is possible since the various properties of a material precisely determine what it is and how it behaves. Some information about the implied relations as well as about the means for analytically deriving behavior equations themselves can be gained by considering the soil as the granular material that it is. Soil is a granular material composed of air, water, and solids. The solid matrix of the soil is built up from stable groups of primary particles (sand, silt, clay) called aggregates or peds. Ag- gregates, or in some instances the primary particles, are arranged in a porous matrix occupied by the air and water. The geometric arrangement of the solid material is generally called soil structure {325). Structure is an independent entity—the fortuitous arrangement of aggregates as influenced by total past history; therefore, structure will have to be measured or identified. A quantitative description of structure probably will be geometric. The description will not be a behavior equation, since structure represents part of the static state of a soil and involves no action. Since structure is an independent entity, its description cannot be calculated from behavior equations, material properties, or any other aspect of soil characterization. Yet structure, together with the mtegrated influence of the material properties of soil, completely determines the specific active and passive behavior of soil when it is subjected to force systems. To illustrate the control that soil structure and material properties have on soil behavior, consider the soil-air system where air is being transmitted through the soil. Obviously, air flows through the porous portion of the soil matrix, and structure determines the size, shape, length, and tortuosity of the pores. Thus, a description of structure will describe the conduits for the air. Since air is the active material of the system, active behavior equations of the air come into play. Air is a fluid, and these equations are embodied in the principles of fluid mechanics. The material properties of the soil also may affect the flow of air. If the structure and material properties of the soil and the active behavior equations of the air were all available in quantitative form, a system of equations would exist. This- system of equations would form a mechanics, as was discussed in chapter 4. The solution of the system of equations would describe the behavior of the soil-air system and provide parameters of the passive role of the soil concerned with air flow. Since the properties of air remain essentially constant, its behavior is essentially constant. Control of the flow of air thus is vested in the structure and material properties of the soil —that is, its condition. SOIL DYNAMICS IN TILLAGE AND TRACTION 305 Theoretically, any passive behavior role could be calculated in this way. A mechanics is formed from the active behavior equations of the transmitted material and a description of soil structure and soil material properties. The solution of the mechanics is the desired behavior equation of the system, and certain parameters will describe the passive behavior of the soil. An active soil behavior equation can be calculated in a similar fashion although the calculation is considerably more complicated. The analogy can perhaps most easily be seen by considering soil structure as though it were a bridge truss. The strength of a bridge is determined by the strength of the elements of the truss and their geometric arrangement. The active behavior is the stress-strain and yield behavior of the elements of the bridge. To calculate the strength of a bridge, the geometry of the truss is described and the appropriate yield conditions of the elements are considered. For soil, the active behavior equations of the aggregates (stress-strain, yield) constitute the active behavior equations of the material m motion. These equations have a function comparable to the transmitted material active behavior equations where the soil participated in passive behavior. When active soil behavior occurs, the action changes the structure. Thus, the structure description will be changing while the active behavior is occurring. It is this changing structure that complicates the calculation of active soil behavior equations. The complication can be seen by again considering the bridge analogy. Unless the bridge truss changes in an orderly fashion as yield occurs, the entire structure will have to be studied as each member fails. A similar situation applies to the soil. The mathematics appears to be highly complex and involved. Thus, while soil behavior equations can theoretically be calculated, the mathematical complexity makes the method seem impractical. The foregoing hypothetical considerations serve two purposes. First, they illustrate the difficulty of making one assessment of soil from which all behavior equation parameters can be calculated. Second, they illustrate the importance of structure and the relation between it and the behavior equation parameters. The relation between soil structure, material properties, and passive soil behavior can be further illustrated by considering water flowing through soil. When water flows through soil, the practical influence of the material properties may be represented by the angle of wetting of the soil. If one assumes that the soil particles are represented by uniform-sized spheres, the radius of the spheres would reflect not only their size but also the surface area of tlie spheres. When the spheres are closely packed, measuring the size of the tetrahedra of the spheres would provide a parameter of structure and size, so that all flow behavior associated with the radius would be reflected by the new parameter. As the soil particles become smaller, the pores and the tetrahedra also become smaller and retard movement of the water through the soil. Since both the size of particles and the structure arrangement of the soil vary, the size distribution of particle radii or pores may be used to describe soil structure. Marshall ( 291 ) has reported encouraging agreement between calculated and measured permeabilities (Darcy's k) of soil 306 AGRICULTURE HANDBOOK 31G, U.S. DEPT. OF AGRICULTURE based on pore size distribution. Thus, structural descriptions may be used to calculate a behavior equation parameter. Considering additional factors should improve the accuracy of the description reported by Marshall. The foregoing oversimplified situation illustrates the fundamental relation between behavior equation parameters and structure and material property parameters. Even though a real situation is much more complex, the fundamental relation is the same ( 239, 2JfO ). Eecognition of this relation is extreraely important, because it indicates some characteristics of soil behavior equation parameters. At first glance, soil behavior parameters would seem to be related to each other since they are nonvarying for nonvarying soil conditions. This implied relation, however, is not directly to each other; rather the relation between behavior parameters is indirectly to each other through the structure and material properties of the soil. Thus, the behavior parameters probably are not related to each other in one-to-one correspondence rules. Eather, they are dependent variables determined by the same independent variables, and these independent variables represent structure and material properties. Unique independent functional relations can exist for the same independent variables, but a unique relation may or may not exist between variables dependent on the same independent variables. The situation is analogous to the one discussed in section 5.2 with regard to the tillage equations. Lack of a direct relation between two parameters greatly restricts the apparent usefulness of behavior equation parameters. Since the parameters are probably not related to each other, one behavior paranieter indicates little about another. In other words, the active behavior parameters will not indicate anything about a passive behavior parameter. In fact, one active behavior parameter probably will not indicate anything about another active behavior parameter. Thus, if only one assessment of soil is to be made, it will have to include the quantities that control the behavior parameters, namely, the integrated effect of structure and material properties. The foregoing discussions indicate not only that the measurements themselves will be difficult to make (measurements of structure, for example) but also that the calculations required to determine the parameters will be even more difficult. ^ The relation also shows that behavior equation parameters cannot indicate anything specific about structure or material properties ; the calculation is not reversible. This nonreversibility is not unique to soil behavior equations. For example, the electrical resistance of a piece of wire does not in any way indicate the size, length, temperature, or material of the wire. Yet these factors precisely determine Its resistance. Thus, the deductive value of behavior equation parameters IS extremely restricted and limited. Behavior equation parameters do assess soil conditions by a means that IS compatible with intended use. When using soil, we are not interested m the structure of the soil or its material properties per se. Eather, we are interested in how these factors affect the behavior involved m our use. Behavior parameters accomplish this one objective. They measure the combined integrated effect of structure, material properties, and any other characteristics that SOIL DYNAMICS IN TILLAGE AND TRACTION 307 affect the behavior under consideration. In short, behavior parameters assess the function of soil in the behavior regardless of how the function is effected. Each parameter or set of parameters is associated with its own behavior and can indicate nothing about another behavior or about the soil itself. The parameter assesses only the factors that are important to the behavior and ignores all other factors. This disregard of factors limits the extrapolation of one behavior parameter to other factors that may be of interest. But this same limitation simplifies the situation so that a useful representation is possible. Behavior parameters thus provide a means for simplifying the complex relation that exists between a material and how it behaves. No easy or convenient means is available for accurately assessing soil conditions. Directly measuring behavior parameters is a simple but not a convenient means unless the intended use of a soil involves few behaviors. When many behaviors are involved, direct measurement becomes inconvenient because each behavior must be individually measured. When the number of measurements is not too cumbersome, direct measurement may be the most expedient method for assessing soil conditions. The limitation of direct measurement is overcome if behavior parameters are related to each other. In the foregoing illustrations, behavior parameters were shown to be indirectly related to each other; consequently, relations cannot be established that would permit measuring one behavior and from it determining the parameters of some other behavior. Behavior parameters were shown to be directly related to structure and material properties. Soil conditions thus can be described in terms of structure if the appropriate relations can be established. Two difficulties limit this approach. First, as the hypothetical illustrations pointed out, the mathematical complexity of the required calculations may make the approach impractical. Second^, even without the mathematical limitation, the measurements required to define a particular structure would be extremely difficult to make. In fact, such measurements could be more difficult and time consuming than numerous direct measurements of many behaviors. Since behavior parameters are related to structure and structure complicates the situation, simplification can be obtained only by simplifymg the description of structure. Composite structure parameters offer a means for simplifying its description. Composite parameters always lack definition and impose a limit on accuracy; consequently, relations between structure and behavior parameters can be determined only by empirical methods. But the representation of structure by composite quantities will simplify the description so that practical relations can be established. Mar- shall's work is an example. Bulk density, percentage of pore space, pore size distribution, and particle size distribution are examples ot composites that are presently used. Perhaps other parameters will need to be identified, isolated, and assessed before satisfactory quantitative measures of structure can be related to behavior parameters. Establishment of composite parameters appears to be the only practical Avay to assess soil conditions other than by direct measurement of behavior parameters. n i j j Since few passive behavior equations have been developed and, 308 AGRICULTURE HANDBOOK 316. U.S. DEPT. OF AGRICULTURE lience, few parameters are available, the relations between structure and the parameters are not available. Consequently, at present (1965), soil conditions are assessed by composite parameters of structure even though the assessments cannot be quantitatively related to the intended use. However, they can be qualitatively related by experienced judgment, and such judgment can indicate the desired magnitude of a composite structure parameter. Thus, the combination of qualitative experienced judgment and quantitative composite structure parameters provides a practical means for de- termmmg tillage tool performance. By these procedures an extremely complex system is simplified at a sacrifice in accuracy. Hopefully, such simplified procedures can be improved and developed step by step until soil conditions can be adequately described and tillage tool performance can be accurately determined and evaluated by quantitative procedures. 6.3 Objectives of Tillage For each use of soil, a separate and distinct soil property or condition may be required. This required soil condition may be modified by circumstances such as climate or economics. Thus, it may become necessary to produce an infinite number of soil conditions by tillage if we are to meet all foreseeable requirements. Be- cause of the infinite number of possible required soil conditions and the lack of quantitative descriptions for these conditions, the reasons for tillage have been used to describe the objectives of tillage. Qualitative terms such as eradication of weeds, pulverization, and smoothing are used to describe the reason for performing a particular soil manipulation. In other words, the kind and degree of changes m the soil—that is, the bases of performance—are not specifically stated as tillage objectives. Qualitative descriptions of tillage objectives will continue to be very useful, but their general nature imposes limitations on their usefulness (SS). They have been useful in developing very specialized tillage tools, each capable of performing some type of specialized soil manipulation. Specialized, yet restricted, descriptions of soil conditions and tools have provided the means for selecting the proper tillage tool to perform a desired manipulation. Just as a craftsman selects a different type of saw for each material he cuts, so must a tiller select a different tool for each soil condition he^ encounters or wishes to establish. In reality, only one objective exists and that is to produce a desired soil condition. The development of quantitative descriptions of soil conditions will enhance the establishment of criteria of performance. In the absence of accurate descriptions generalized purposes of tillage may be classified for use as objectives of tillage. A summary of the common objectives of tillage follows: 1. CONDITIONING OF SOIL: Tillage is performed to loosen, granulate, or otherwise condition soils. Often this is done to promote plant growth. Soil may be cut, loosened, or broken up so that it may be moved or so that water and air may move more freely through it. Soil may also be loosened to promote drying or to reduce the mechanical strength of the soil mass. SOIL DYNAMICS IN TILLAGE AND TRACTION 309

2. ERADICATION OR CONTROL OF PLANTS OR PLANT MATERIALS : Tillage is frequently performed to control weeds during the production of crops. Sometimes weeds are controlled by chemical means. On the other hand, the complete removal of plant materials—as m the creation of a firebreak—may be required. Plant thinners that operate in the soil control plant growth. Not all mulching operations involve soil tillage; some operations merely process plant residue. 3. ESTABLISHMENT OF SOIL BOUNDARIES AND SURFACE CONFIGURA- TIONS: In planting (listing and bedding), irrigation, drainage, and landscaping, the soil often is tilled to create some special soil configuration on or in the soil profile. These tillage operations would generally fall in the class of land forming, but this would not preclude the inclusion of a ditch cleaner since its action would be to restore a desirable boundary by moving the soil (^5). Transient boundaries may be used to inñuence soil-handling operations. For example, a coulter or jointer may be used to establish a clean or straight boundary to promote good plow action. The boundary is transient since it may be removed within a few seconds after it is established. 4. INCORPORATING, COVERING, OR HANDLING FOREIGN MATERIALS IN SOIL: Fertilizers, plant residues, mulch papers, soil amendments, ñexible pipes, communication wires, military mines, and many other materials may be inserted into the soil by tillage. Often these materials are distributed in specific portions of the soil profile so that the designs and principles of use of tillage tools may vary considerably. The inversion of soil by tillage in order to cover materials such as crop residues or radioactive dust may serve no other useful purpose even though granulation and other effects of the operation may be obtained as a byproduct of the primary action. 5. SEGREGATION: Tillage may be used to move soil or other materials from one layer of soil to another. This occurs when deep tillage is used to create clods and to move these clods to the surface in order to minimize wind erosion. Segregation may also involve the removal of materials from the soil. Kock picking and root harvesting are included in this category. 6. MIXING: When incorporating materials into the soil, some type of mixing is frequently needed. This may be done to promote drying of the soil, to mix moisture throughout a depth of soil, or to distribute amendments such as soil conditioners, fertilizers, or soil- stabilizing materials. In special cases, several layers of soil may be mixed to form a different, more desirable soil texture. 7. COMPACTION OR FIRMING: There are a number of situations such as in the construction of foundations where the strength of the soil must be increased by compaction. In addition, compaction niay be used to decrease the permeability of the soil to water m order to make water-retaining structures such as ditches, terraces, or dams. The manipulation of soil by means of a roller or tamper is a widely used form of tillage. Firming operations are needed to gam good contact between seeds and the soil in seedbed preparation. In this case the mechanical strength increase may be detrimental while the added contact is desirable. 310 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

6.4 Measuring Performance The specific performance of a specific tillage tool cannot be calculated at present; sufficient knowledge has not been developed. But limited aspects of performance can be measured, and these measures have been used in developing tillage tools that can effect acceptable changes in soil conditions. As indicated in section 6.1, the tool forces and the change in soil conditions are the two basic aspects of tillage tool performance. Tool forces are relatively easy to measure. The change in soil conditions can be easily described in some situations. Such a situation occurs when soil is to be rotated or moved en masse into a new location or position. Another occurs when a plant residue on the soil surface or a surface layer of soil is to be placed at a different position m a soil profile. When soil conditions can be simply described, changes in conditions can be easily described and performance can be measured. Even though soil conditions cannot be easily described, tool forces can usually be measured. Soil conditions in these situations are usually determined only in a qualitative sense; often no measurement IS made. Considerable data have been reported dealing with forces measured on tools during tillage. Often nothing is reported to indicate that the soil condition was changed. The reader can only assume that the tool, say a moldboard plow, was qualitatively noted to be manipulating the soil in a satisfactory manner while the tool torces were being measured. Presumably,^ until quantitative descriptions of the change m soil conditions are identified and can be measured, measures of performance will have to remain quantitative m some aspects and qualitative in others. Some of the devices and techniques that have been used to measure performance are discussed in this section. Measurements of performance are, of course, based on the same measurements that need to be made for empirical studies of tillage tool design. This occurs because criteria of performance reflect precisely the same quantities that are used m tillage tool design. Measurements discussed in this chapter illustrate methods and techniques that are useful in descriptions of performance rather than design. Improving present metiiods and techniques and developing new ones provide formidable challenges for future research. 6.4.1 Forces A tillage tool is subjected to three independent force systems, i hese systems are the weight acting at the center of gravity of the tool, the soil forces acting on the tool, and the forces acting between the tool and the prime mover. These force systems are in equilibrium if no acceleration is involved. Since the soil forces are determined by the soil-tool system (the forces represented in equation 132), and tool weight can be considered constant, the forces acting between the tool and the prime mover "adjust" so that equilibrium IS maintained. If the prime mover is replaced by a dynamometer, and the weight of the tool is appropriately considered, soil forces on a tillage tool can be measured. Although the principle of measuring soil forces is direct, actually SOIL DYNAMICS IN TILLAGE AND TRACTION 311 obtaining meaningful measurements is not. Soil conditions, tool shape, and manner of tool movement directly alïect soil torces (equation 132). Except for wear, tool shape remains essentially unchanged for a tool; but the manner in which the tOT)l is moved through the soil is controlled by the dynamometer. Iheretore, a dynamometer must not only be able to measure the forces between itself and a tool, it must also be able to hold the tool m position so that the tool's depth, width, and orientation do not change during operation. Because the condition of soil at any particular location cannot be quantitatively expressed with accuracy, and because ot the wide variability in soil, soil conditions must also be controlled by soil preparation techniques. Variations between two areas within one field may cause greater ditïerences in measured forces than the difference caused by two different tools. Experience has shown that control of soil conditions is essential; hence, elaborate facilities ot the type described in chapter 1 have been devised and constructed. In these facilities bins of uniform soil material are maintained to provide more uniform plots of soil than can be found naturally m the field. , , ^ -, -, One of the early recording tillage tool dynamometers was devel- . i/=

~~v = V4=5:(v,.v,.av8) Vsb X » VALUE OF COUPLE = Va~~

~~T(V| ±V2) (A)~~

FIGURE 214.—Designation and reduction of forces on a tillage tool. (Clyde, Pa. Agr. Expt. Sta. (77).) 312 AGRICULTURE HANDBOOK 31«. U.S. DEI'T. OF AGRICULTURE oped by Keen and Haines at Rothamsted Experiment Station in Entrlund {215). Most of the early dyiianionieters were hydraulic units, but many of tliese have been replaced by units employing electric resistance strain gages. A number of dynamometers have been described in detail ( 75. IJ4. 3.^7. .¡81. .i82 ). Clyde ( 76. 77 ) pioneered nuich of the early research in the Ignited States in measuring forces on tillage tools. lie used a portable g>üde rail 240 feet long to control the path of a tool, and he measured the six forces reipiired to restrain the six degrees of freedom of a tool. The location of the restraining forces and the method for vectorially combining the forces and for locating the line of action of the resultant force is shown in ligure iil4. The physical locations of sensing devices used by Clyde were at the apices of the horizontal equilateral triangle. Distances h and c in figure 214, A are schematic, btit they represent the lai'ge physical distance between sensing elements in many hydraulic dynamometers. T'se of electric resistance sti'ain gages has conveniently reduced distances h and r by a factor of approximately 10, so that nioi'e comi)act dynamometers can be developed. Figure 21.") shows one short-distance arrangement developed at the National Tillage ^fachinery Laboiatory. No one method has been widely accepted oi- considei-ed to he superior for reporting forces on tillage tools. Figuie 21() shows a convention proposed by Clyde that orders and identifies forces and "%flT

~~FIGURE 215.—A dynamometer employing .«train gages for measuring soil forces on tillage tools. SOIL DYNAMICS IN TILLAGE AND TRACTION 313~~

~~TRAVEL~~

~~SOIL FORCE ON TOOL COUPLE OR MOMENT~~

DESIGNATION SYMBOL ^o^'^'^^s '^'^ ^^^^^^ ^^^•'^^^^ DIRECTION ^ ^ CUXKWISE LONGITUDINAL L X X MX Z Y, LOOKING AHEAD _ ^ CLOCKWISE SIDE S Y Y MY Z X, LOOKING LEFT w v/ CLOCKWISE VERTICAL V Z Z MZ X Y, LOOKING DOWN

FIGURE 216.—Designation of forces and moments on tillage tools. (Clyde, Pa. Agr. Expt. Sta. ( 77 ).) moments with respect to a coordinate axis. The convention avoids confusion, and there appears to be no cogent reason tor changing it except that it is not compatible with principles of vector ana ysis. A right-handed coordinate system is required by vector ana ysis, and the direction of the moment designated MX m figure 216 is reversed in a right-handed coordinate system. Rogers ( Sll ) reports that five methods have been used to express forces on a tillage tool. These methods are : 1. A wrench—that is, a force with a couple m a plane perpendicular to the force. -VA 2. A force through a chosen point and a couple m a plane mclmea to the force. 3. Two forces, one on a chosen line. 4. Three forces on mutually perpendicular axes and three couples in the planes of intersection of the axes. 5. Three forces in three major planes. Results may be accurately reported by any of these methods, mt one method may be more desirable than the others, depending on the intended use of the data. If, however, one is mterested m the location of the resultant forces, only one method accurately locates the resultant force. The resultant force does have a unique line ot action; this location should be known for research and design pur- ^^Vanden Berg ( ^55 ) has used vector analysis to show that reducing forces to a wrench determines the unique line of action, i he true line of action of a resultant force represents the mmimum couple for a system of distributed forces and, hence, the wrench is independent of any arbitrary reference point or reference plane. Any of the methods of reporting can be reduced to a wrench to locate the unique line of action. 314 AGRICULTURE HANDBOOK 316, U.S. DEPT. QF AGRICULTURE Because of the lack of well-defined criteria of performance, measurements of the distribution of forces over the surface of a tool have been used to reflect performance. If the distribution is uniform or constitutes some pattern that is believed to be desirable, the performance of the tool is considered to be desirable. Measurement of the distribution of forces over the surface of a tool also provides knowledge that is needed to understand the interaction of tool and soil. Little research has been done to determine distribution, but this has been due in part to the lack of adequate instrumentation. One of the earliest attempts to measure surface pressures on a tool was made by Mauer ( 294 ) in 1933, when he embedded a small pressure transducer m a chisel. He measured the pressure at only one location and showed that it correlated with the total draft required to pull the chisel through the soil. Figure 217 shows the cor-

~~UJ (T (/) (/) UJ cn a.~~

~~oÜJ ¡2 01~~

~~DISTANCE (in)~~

~~FIGURE 217.—Draft and surface pressure of an inclined chisel as related to distance of travel. (Mauer, Auburn Univ., ( 294 )•)~~

relation of pressure near the tip and the draft. The cyclic nature of the curves coincided with the development of major shear failures m the soil. Mauer also investigated the relation between the lift angle of the chisel and the maximum measured unit pressure as affected by soil preparation factors, moisture content, and the pressure used to compact the soil. The data in figure 218 show that any factor that increases the draft of the tool also increases the pressure on the surface of the tool. Instrumentation techniques have improved considerably since Mauer's work, but even recent studies ( 332, ^19 ) have not produced detailed information about the distribution of pressure on the surface of a chisel. Mayauskas ( 295 ) has determined the pressure distribution on the surface of a plowshare. A series of pressure transducers were placed m a pattern so that simultaneous measurements could be made (fig. 218), and a series of experiments were conducted in which the instru- SOIL DYNAMICS IN TILLAGE AND TRACTION 315 PRESSURE OF 10 SOIL COMPACTION 10 /"^ 7psi

~~Q. 8 - 3 8 UJ LÜ a: 5psi £r (/) 6 (/) 6 UJ UJ a: Q_ Q. 2 4 S 4 3psi 3 X< < 2 2 S 2~~

~~15 25 35 45 18 22 26 30 ANGLE n MOISTURE (7o)~~

FIGURE 218.—Effect of lift angle, moisture content, and pressure to compact soil on the maximum pressure in the tip of an inclined chisel. (Mauer, Auburn Univ., ( 294 )•) mented plowshare was used. The results (fig. 220) show the manner in which the factors investigated inñüence the magnitude and distribution of pressure on the surface of a share. No information is available to indicate what magnitude or distribution ot pressure can be considered to be good performance. Certainly, however, criteria could be developed and performance measured m terms ot the distribution and magnitude of pressure on the soil-engagmg surface of tillage tools. Measurements of this type have been made in several countries. . . In another approach directed toward measuring performance, an attempt was made to separate the draft of a moldboard plow into

FIGURE 219.—Position of pressure transducers in a plowshare used to determine pressure distributions. (Mayauskas, Traktory i Selkhozmashiny (295).) 316 AGRICULTURE HANDBOOK 316, US. DEPT. OF AGRICULTURE SPEED (m/sec) DEPTH (cm) ^-0.8 1—17 I-KNIFE COULTER ^"'•' 2—22 2-DISC COULTER ^'"'•'^ 3—27 3-NO COULTER

~~4 4 -^ 4 -^ ■ \ 3 3 -^ 3 I\\ 2 -ß 2 2 - vvsii^^y^ 1 1 I P^^^o o 1 —1—1—1—1—1—1—I 1 1 1.0 2.0 3.0 4.0 1.0 ^0 3.0 4.0 1.0 2.0 3.( PRESSURE (Kg/cm*) (A) (B) (C)~~

~~FIGURE 220.—Average pressure at locations 1, 5, 8, and 11 in figure 219, as SoLthfny^^^^^^^^ '^^^' '• ^' ''^' ^^ ^^^^^^^^- (Mayauskas, Traktory i~~

portions required to cut, pulverize, and invert soil. This was done by cutting a plow into sections and measuring the draft of the sections as they were progressively added together (table 37). The data indicate that the final one-fourth of the moldboard did not materially add to the draft at either of the two speeds studied. This final section, however, may have been of paramount importance in obtaining adequate inversion of the soil. Pounds of draft per se, therefore, cannot be used as the sole criterion for performance. As was the case tor surface pressure distributions, no standards are available to indicate whether the performance indicated in table 37 is desirable At the very least, however, the data are useful for a qualitative understanding of the interaction of tool and soil. A tool inclined 3°, together with a wire, has also been used in an attempt to separate cutting, sliding, and shearing actions for a simple

~~TABLE Z1 ,—Contribution of différent segments of a plow to the draft force~~

Speed of plowing 2 m.p.h. 3 m.p.h. Segment of tool Fraction Fraction Draft of Draft of force total force total draft draft Pounds Perceyit Pounds Percent Wire (to represent plow edge)_ 44 23 59 26 Half share 97 51 101 44 Full share 154 81 181 79 Full share + 3/4 moldboard 187 99 212 92 Complete plow 191 100 230 100 SOIL DYNAMICS IN TILLAGE AND TRACTION 317 tool (352), The draft force required to pull a wire through soil, as shown in figure 77, may be interpreted as being the force required to cut or separate the soil slice from the semi-mfinite undisturbed mass of soil. The thin, ñat blade operated at a lift angle ot 3 separates a mass equal to the mass of soil separated by the wire. The total force both cuts the soil and overcomes the friction ot the soil sliding over the upper surface of the blade. The 3° lift angle provides clearance so that friction does not occur on the lower surface of the blade. . i p^ j! ^i. The difference between the draft of the wire and the dratt ot the inclined blade was assumed to be due to soil-metal friction. It the blade is operated at a lift angle of 221/2° or 45% the ridge of soil will not only shear but also pulverize. The draft of the blade may be thought to be composed of forces required for cutting, sliding (friction), shearing, and accelerating the soil. on-. j The difference between the drafts of the wire, the 3 blade, and a blade with a higher lift angle permits separation of the draft components required for cutting, sliding, shearing, and accelerating the soil. Figure 221 shows the measured forces as a function ot speed

~~500~~

~~400~~

~~300 < a: Q 200~~

~~100~~

~~SPEED (mph)~~

~~FIGURE 221.—Effect of speed on the draft of a wire and a flat inclined plate.~~

as the wire and blade were operated in a clay soil. These forces may be separated into the relative contributions of cutting, sliding friction and shear plus acceleration. Visual observation indicated that the amount of soil breakup was nearly the same when the blade was inclined 22i/4° and 45°. Figure 222 shows the contributions ot the various actions when the draft of the 221/2° blade was assumed to represent the total required draft. It appears that speed greatly influenced the relative contributions of the origins of resistance, ihe high percentage of draft that can be attributed to cutting is also significant. Cutting represented a large component of the dratt ot the moldboard plow reported in table 37. 318 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE CUTTING

~~SHEAR + ACCELERATING~~

~~SPEED (mph)~~

~~FIGURE 222.—Relative contributions of cutting, sliding friction, and shearing plus acceleration to the draft of an inclined tool operating in a clay soil.~~

Many measurements with various types of dynamometers have been made of soil forces on tillage tools, and the measurements are readily available to tillage tool designers ( 98,171,179, 202, 237, 262, 387-389, 506 ). Each force measurement represents a limited measurement of the performance of the particular tool for the particular conditions under which it was operated. In a similar manner, measurements of pressure distribution and of the separation of draft into components are measures of tillage tool force performance for the situations studied. In general, the smaller the forces or pressures the better the performance. But the amount of soil manipulation must also be considered because it may alter any conclusions that are based on forces alone. Future measurements of force performance will probably be made with techniques and equipment similar to those reported here. 6.4.2 Soil Conditions Soil conditions cannot presently be quantitatively described. In the past, the reasons for tillage have emphasized the manner in which soil conditions should be changed rather than a description of the conditions that should be changed. Some attempts have been made to describe objectives of tillage in more quantitative terms. Soil breakup, segregation, and mixing are the three objectives that have been measured and used to determine the performance of tillage tools. ^ Quantitative descriptions of soil based on what is done to the soil are useful in measuring performance. Such descriptions are a stopgap procedure, however, and they should be used only as a last resort. Their limitation is not that they cannot be developed to provide an accurate description; rather, their limitation is that they usually cannot be directly related to the intended use. While soil breakup SOIL DYNAMICS IN TILLAGE AND TRACTION 319 is certainly important for plant growth, describing the amount of breakup will not directly describe soil conditions in terms compatible with plant growth needs. Terms compatible with plant growth are defined by the soil behavior equations that influence plant growth. Unless an objective of tillage is measured in terms that are directly related to an intended use of a soil, the measurement will have limited usefulness. 6.4.2.1 Breakup The amount of soil breakup by tillage tools can be determined by a sieve separation of the soil. Sieving provides a simple means for measuring the range of clod sizes and the relative amount of soil in each size class ( 101, 130. 452 ). Figure 223 shows a rotary sieve for separating clod sizes of a

~~FIGURE 223.—Rotary sieve for separating fragmented soil into various sizes.~~

fragmented soil. Slowly rotating the cylindrical sieve provides a gentle sieving action so that any breakup of the soil due to the sieving action is minimized. The relative amount of each size group can be determined either by weight or by volume, and some average or modulus can be calculated to represent the distribution. One representation often used, for example, is the mean weight diameter of the clods. The mean weight diameter can be calculated by constructing a graph of clod size versus an accumulative percentage by weight of the clods found in increasing size classes. The area under the resulting curve can be obtained by a polar planimeter or some other means, and the mean weight diameter is calculated by dividing the area by the range of clod size that was considered. A number of similarly determined averages have been used by various researchers. Yoder ( 514. ) ^vas one of the first to use this technique to measure breakup. 320 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE These techniques give only a relative measure of soil breakup. An absolute measure of change can be obtained by determining the clod sizes before and after a manipulation. Many times soil cannot be sieved before manipulation since it is a semi-infinite cohesive mass that IS essentially one clod. Since types of manipulation are usually compared m the same soil condition, the initial clod size can be assumed to be constant even though it is not known. Final clod size thus IS a relative measure of the amount of breakup, and performance can be measured and assessed on a comparative basis. The sieve separation of clod sizes has been used by several workers to measure breakup performance of tillage tools of different designs. Gill and McCreery ( IJß ) have shown that the size of cut is an important factor for drawn tools, whereas Frevert {135), Adams and Furlong ( 7 ), and Umeda ( U5 ) have reported its importance for rotary tools. The size of cut of a tool may be altered by changing either the width of the tool or its depth of operation. Figure 187 shows the experimental tools used by Gill and McCreery to vary the width of the tool and hence the size of cut. For a compacted clay soil, the data indicate the general trend that the smaller the cut, the smaller the resulting clods (table 38). Figure 224 shows the clod sizes that

~~< 2 o~~

~~UJ < a: ÜJ~~

~~12 3 4 5 6 7 DEPTH OF CUT (in)~~

FIGURE 224.—Effect of depth of cut of a rotary tiller on the size of clods in a silt loam soil. (Adams and Furlong, Agr. Engin. { 1 ).) resulted when the depth of a rotary tiller was varied. The data appear to contradict those in table 38, since clods were smaller at deeper depths of operation. Because the movement of drawn and rotary tools differs, the data may not be in conflict. The depth of operation of a rotary tool may be changed without greatly altering the size of cut. A change in either forward speed or rotor speed materially changes the size of cut. Furthermore, a vertical gradient usually exists in moisture and strength in a soil profile. Soil at the deeper depths may fragment easier so that smaller clods result. In SOIL DYNAMICS IN TILLAGE AND TRACTION 321

~~TABLE 38.—Effect of the size of cut on the mean weight diameter of clods produced in a compacted clay soil~~

~~Size of cut Clod size in mean Tool by tool weight diameter Inches Inches Plow and coulter 1 1.47 2 3.55 4 6.46 6 7.07 8 8.61 Disk plow 1 1.76 2 3.66 4 4.49 6 4.19 8 4.15~~

1 SOURCE : Gill and McCreery {IJ^d ). any case the importance of size of cut on soil breakup is demonstrated and the technique of sieving provides a useful measure of breakup. Soil breakup as measured by sieving has been used to study the effect of impact on breakup. Tillage tools can and do impart considerable energy to soil through impact. If the transfer of impact energy is great enough, fragmenting of clods may result. To isolate the effect of impact, the size of cut must be maintained constant. Maintaining constant size of cut is relatively easy with drawn tools,

~~tr 3~~

~~LÜ < Û~~

~~û: ÜJ~~

~~200 600 IODO 1400 ROTOR PERIPHERAL SPEED (Ft/min)~~

FIGURE 225.—Effect of increased impact energy on clod size for various sizes of cut of a rotary tiUer. (Adams and Furlong, Agr. Engin, (i).) 322 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE but rotor speed and forward speed must both be carefully controlled with rotary tools. By increasing the forward speed in accordance with the rotor speed, a uniform size of cut can be maintained with a rotary tiller. Figure 225 shows the results oï an experiment where the depth of operation was 4 inches and several sizes of cut were used. As the rotor speed increased, the cutting speed of individual tmes increased so that they passed through the soil in less time. Higher speeds produced greater impacts. The data show that as the impact increased, the average clod sizes decreased even though the size of cut was constant. Table 39 shows .a similar trend for drawn tools. The change in speed and, hence, change in impact is much less for the chisels reported in table 39. The change in breakup is also less, but the data show that increased impact causes increased breakup.

~~TABLE WI.—Effect of speed on the size of clods produced hy chiseling~~

~~Clods greater than 19.2 millimeters in diameter Percent 31.7 30.8 28.2 8.3 5.8 5.3 SOURCE : Woodruff, Chepil, and Lynch {511).~~

6.4,2.2 Segregation Nothing in section 6.4.2.1 describes the final location or position of soil clods in the soil profile ; emphasis was on a description of the change of clod size. Tillage is sometimes undertaken to control the distribution of clods within the profile. For example, large clods may be placed on the surface of a soil because they tend to prevent wind erosion ( 510, 511 ). On the other hand, small clods are usually desired in the vicinity of seed to provide an optimum environment for germination. In such instances tillage tries to segregate soil according to clod size or some other criterion that will improve the condition of soil. Sieving distinct layers of the soil profile provides a means for measuring the segregation performance of tillage tools. The action of narrow tines on tillage tools such as harrows segre- gates clod sizes. Winkelblech ( 507 ) used the sieving technique to study the effect of several common tools on the distribution of clods in a soil profile that was uniform before tillage. He used a pulverization modulus proposed by Yoder ( 5H ) to express clod size. The modulus is essentially a weighted average ; the average is so weighted that the resulting modulus reflects an average clod size in a sample. Winkelblech used size classes li/4 to % inch, % to % inch, % to %6 inch, %g to %2 inch, and less than %2 inch. To calculate the pulverization modulus, the percentage of soil in each size class is multiplied by an ordered weighting factor. Winkelblech used zero for less than %2 inch, 1 for %6 to %2 inch, and on up to 5 for the SOIL DYNAMICS IN TILLAGE AND TRACTION 323 largest size. The weighted percentages were summed and divided by 100 to give the pulverization modulus. Thus, if all the clods were in the largest size, the calculated modulus would be 5. On the other hand, if all the clods were less than %2 inch, the modulus would be zero. Winkelblech determined the pulverization modulus for 1-inch increments of depth in an experimentally prepared soil after it was tilled to a depth of 4 inches. The untilled soil had a uniform modulus at all depths. Figure 22^6 shows the segregation of clod sizes that PULVERIZATION MODULUS

~~SPRING TOOTH z 1-2- DISK 18*» DISK 28** Q. SWEEPS, 10" ÜJ O 2-3~~

~~-UNTILLED~~

~~COARSER~~

~~FIGURE 226.—Segregation of clod sizes by various tiUage tools in an experimentally prepared soil. (Winkelblech, Ohio State Univ. {507 ).)~~

resulted from the soil manipulation caused by two passes of various tools. The larger clods moved to the surface while the smaller clods concentrated in the deeper layers. A significant point is that all tools had essentially the same sorting action. Factors that affect mixing and sorting of solids have been studied by Fischer (117) and Weidenbaum (500), but the factors have not been applied to the actions of tillage tools. Possibly the original distribution of clod sizes determines the segregation that will occur, regardless of the type of tillage. In Winkelblech's experiment, essentially no additional breakup occurred because of the harrowing; the range of clod sizes before and after tillage was essentially the same. The effect of tillage was merely to rearrange the distribution. If the original distribution determines the nature of resulting segregation, then the original distribution (the breakup) will have to be controlled in order to control segregation. A different principle of segregation of soil is illustrated m figure 227. A tool of this type was specifically designed by Boetha as cited by Nichols and Keaves (322)^ to operate in a soil that had a sandy surface underlain by a clay subsoil. By controlling the depth of the tool, the wedge action described in section 4.3.2 moved a wedge of clay soil upward along the surface of the tool so as to deposit the clay on the surface of the soil. By controlling spacing and depth of penetration, a predetermined amount of subsoil can be transported 324 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~xxxxxxxxxxxxxxxxxxxxxxxxxxxxx~~

~~FIGURE 227.—Segregation of subsoil to the surface to permit soil renovation.~~

to the surface. Clay transported to the surface is then mixed into the surface with conventional tillage tools to complete the renovation of the soil. Segregation is essential in order to effect this type of soil renovation. Two means of segregating soil have been discussed. They lack the positive control that is possible with sieves. Sieves not only provide a means to measure segregation performance, but they also are a means for effecting segregation. They have not been used much because of the difficulty of obtaining a large output. The principle, however, is sound and its lack of use in the past should not be a deterrent to further consideration. Johnson ( 203 ) has designed a plow-type sieving device to demonstrate that sieves can be practically used. With this device, soil is lifted with a simple blade and then moved by an auger through slotted troughs. The slots are sized so that small clods pass first and larger clods are retained. The troughs are angled as shown in figure 228, so that fine soil is retained in a row to provide a

~~CLOD ARRANGEMENT~~

~~AUGERS~~

~~LIFTING BLADE~~

~~^SIEVE SLOTS~~

FIGURE 228.—Device for separating sizes of clods. SOIL DYNAMICS IN TILLAGE AND TRACTION 325 seedbed while large clods are placed between rows where control of erosion is important. The device utilizes small clods that are already present to form a seedbed so that additional energy is not required to further break soil into small clods. The principle of segregation of clod sizes may save more work in tillage than any other principle that has been proposed. The positive control permitted by sieving may make the principle practical. Sieving thus is not only a means for measuring segregation performance ; it is also a means for effecting the performance. 6,4,2,3 Mixing Often an objective of tillage is to mix the soil to obtain uniform distribution of moisture or clods—that is, a nonsegregated soil condition. In other instances, granulated material similar to soil aggregates, such as fertilizer, needs to be mixed with soil. Uniformity of mixing is a measure of mixing performance. Tracer materials have been used to measure mixing performance. Wooten, McWhorter, and Eanney (512) used fluorescent materials that could be photographed to obtain a graphic representation of the degree of mixing. These workers reported that at least three disk- ings are required to adequately mix material that is applied to the surface. Hulburt and Menzel ( 188 ) used grain sorghum and radioactive phosphorous as tracer materials. The tracer material was located by excavating to expose a vertical profile of the soil for observation or sampling. Figure 229 shows the results of two tillage treatments in which grain sorghum was used as a tracer material. Eotary tilling should be done at least twice, according to Hulburt and Menzel, to obtain adequate mixing. Tracer materials provide a convenient means for measuring mixing performance.

~~GROUND ¿SURFACE c I -. t 5- 7 K 30in •~~

~~FIGURE 229.—Distribution of grain sorghum tracer materials : Left, After plowing and harrowing; right, after rotary tilling. (Hulburt and Menzel, Agr. Engin. (188).)~~

Attempts have been made to express the distribution of mixing in some mathematical form so that the degree of mixing can be evaluated. Graphical representation does not quantitatively represent the degree of mixing (fig. 229). Smith {39S) has used a mixing coefficient R to express the degree of mixing. He defined this coefficient as the ratio of the standard deviation at zero mixing to the observed deviation. The definition is particularly appropriate where, in the initial condition, one layer of material is located over another 326 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE SO that a sharp boundary exists between them. The coefficient in this situation is 1, and it represents no mixing. The coefficient approaches infinity as the mixing becomes more uniform. The coefficient R is defined as :

~~(152) 2 {Xi-ü,y~~

where N - number of spot samples taken from a mix containing a mean fraction of additive JJa^ Xi = indicated content of any sample, CTn theoretical standard deviation at zero mixing, V¿Va(l-¿/„), standard deviation at any time, {x,-üay n This coefficient may be useful when fertilizer or some similar granular material is to be mixed in soil. The approach can be modified to suit other situations. The concept, however, provides a means for expressing mixing by a single number and so provides a means to determine mixing performance. 6.4.3 Specialized Tillage Actions In section 6.4.2, several means were discussed of measuring tillage perforniance where emphasis is placed on the condition of the soil. Often tillage involves a specific action where condition of the soil is of secondary importance. Since these actions are usually highly specialized, they are classed here as specialized tillage actions. Ex- amples are handling plant residue, inserting foreign materials such as dram tile or electric cable into soil, and separating root crops such as potatoes or sugar beets from the soil. Since soil condition is of secondary importance, performance is concerned with forces required to operate the specialized tillage tool and with the completion of the intended action. Often the action does not require a numerical description of the degree of completion; either the action is performed, or it is not. For example, either an electric cable is buried in a suitable operating position, or it is not. Measuring performance of specialized tillage actions is often relatively simple when compared with measuring performance where soil condition is of interest. If desired, degrees of success might be introduced m terms of the number of cable breaks per mile, the number of points of inadequate depth of placement, or some other limiting condition. 6.4.3.7 Handling Plant Residue Tillage is often performed where plant residues are encountered. In some instances the residue must be handled only to prevent its interference with the operation of the tillage tool. Usually, however, SOIL DYNAMICS IN TILLAGE AND TRACTION 327 the residue is to be incorporated into soil and handling requires more than just preventing interference. Plant residues are occasionally handled by auxiliary devices used with a tillage tool. The most widely used attachment is probably the coulter that is associated with a moldboard plow. The use of auxiliary devices is a departure from the philosophy that a single tool can be pulled through soil to accomplish everything that is desired. When soil conditions are to be changed, such a philosophy can probably be applied without any theoretical limitations. When specialized tillage actions are involved, however, theoretical as well as practical limitations suggest that a multistage action is required to accomplish the intended change. In such instances, multiple tools probably will best meet the requirements. The performance of auxiliary devices has received considerable attention. One reason is that the performance can be assessed without measurements. Coulters, for example, perform a definite cutting action that severs plant residue. Cutting changes the dimensions of the residue so that its maximum width is the width of a furrow slice. With the plant material cut, the natural action of lifting and turning a furrow slice by a moldboard plow is not hindered, and the residue is covered by the soil. Performance of the coulter, therefore, can be easily determined without measuring by observing how effectively the material is cut. A number of variations of coulters have been used. Knives, notched coulters, and disks have been designed for use with moldboard plows. Notched coulters have been powered to act as a saw, and it has been reported that they are effective in cutting heavy trash {390), The unpowered notched coulter traps the plant material so that it is cut as the coulter attempts to force it into the soil. This trapping action minimizes the bulldozing of the residues that decreases the cutting effectiveness of a coulter. For effective cutting, the soil conditions must be firm ; otherwise, instead of being cut the material will be crushed into the soil. The crushing action has been utilized with blunt tools to anchor plant residue to the surface of soil in order to minimize wind erosion {73), Disk packers with spaces of 4 to 6 inches were effective in pressing plant materials into soil to control erosion. A jointer is another auxiliary device that has been used in handling plant residue. A jointer moves a portion of the surface residue toward the open furrow. This detached residue is literally thrown into the bottom of the furrow and covered. A jointer also tends to break up the soil it contacts, but its primary purpose is to aid m handling plant residue. A combined coulter and jointer handles plant residue effectively. Plant material that is extremely long or that lies parallel to the direction of travel, so it is not cut by the coulter, can often be oriented by means of a wire or trash guide. These devices guide the material along an intended path or press the material tightly against the soil so that it is covered by the soil during plowing. Performance of devices for handling plant residue usually is not measured; it is determined by the effectiveness with which the residue is handled. Figure 230 shows how three plowing techniques place surface resi- AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

FIGURE 230.—Location of plant residue In soil after tillage: A, With a moldboard plow equipped with coulter and wire, plowing 8 inches deep ; B, with a low-speed moldboard plow, plowing -ly^ inches deep; and C, with a disk plow, plowing 4% Indies deep. SOIL DYNAMICS IN TILLAGE AND TRACTION 329 due in tilled soil ( 348 ). One must decide on the desired placement before the appropriate technique can be chosen. In situation A^ the plant material is placed in thick isolated bands so that continuity of the soil is retained through the profile. In- situation B. the plant residue essentially isolates the plowed layer from the subsoil. In situation C, the plant residue is inclined vertically so that the residue is in continuous contact from the surface to the subsoil through the tilled layer. This increases the rate at which water infiltrates both the soil and the plant residue. Jamison ( W^ ) has reported that complete isolation of the tilled layer by a continuous mat of plant material in the bottom of the furrow may impede the movement of moisture through soil. Thus, the intended use of soil must be considered before the desired condition can be created by selecting and using tillage tools. (^overing plant materials is one of the important requirements of tillage. The covering requirement establishes the need for a tool that inverts soil ; the moldboard plow is superior to all other tools in this respect. Recently an attempt has been made to improve the coverage capabilities of disks. A disk with a recurved center (fig. 231) has been developed for this purpose. The recurved center induces a turning movement to the surface of the disturl)ed soil, which improves coverage. To be eifective, the recurved disk must be

FiQUBE 231.—A recurved disk designed to improve inversion of soil. 330 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE operated at such a depth that the recurved center influences soil movement. An interesting sidelight of plant residue is its potential effect on the strength of soil ( 327, il6 ). unfortunately, few measurements of this tj^pe have been made, but the data in table 40 clearly indicate that the influence can be significant.

~~TABLE 40.—Increase^ in soil strength caused ly the incorporation and compression of various plant materials in the soil~~

Plant Compressive Increase in material strength strength P.s.i. Percent Oat strawi 485 49 Flax straw _ _ »_ __ 473 45 Grass sod 357 9 None_ _ 325 This material was chopped into pieces 5 inches long and added to the soil until It began to bunch up in the soil and reduce strength. SOURCE : Patty and Minium {S21 ).

6.4.3.2 Insertion of Foreign Materials Into Soil Foreign materials frequently need to be inserted into the soil in a continuous form rather than in the more common discontinuous form used to insert fertilizers, plant residues, or soil amendments. Eecent technological developments have created the need to place communication wires and irrigation or drainage pipes underground quickly and economically. As an example, the use of robot agricultural tractors that can be controlled electrically from underground wires would permit a higher degree of automation. In the past, a trench was excavated so that large underground lines could be properly installed. Today, many current requirements can be met with small-diameter lines (^6), These materials can be inserted into the soil by special tillage tools that have a wide shank containing a channel through which the material is lowered to the desired depth. Performance is easily determined where continuous materials are inserted into soil. For a wire, which does not require the precision type of elevation control that a gravity drain system requires, the passage of the tool at some designated depth below the surface insures satisfactory placement. Only the conductivity of the inplace wire need be measured. Forces that cause the tool to pass through the soil are, of course, measured and are important. In several studies the performance of specialized tools designed to place communication wires underground has been measured. Much communication wire is laid in occupied residential areas where there is a need to leave the soil in an essentially undisturbed condition. The direction in which forces are applied to soil deter- nimes the soil reaction (fig. 232). A tool operated with an angle of approach of less than 48° usually results in an upheaval of the soil and an unsightly appearance after the operation (fig. 232, A). If the approach angle is increased above 132°, the main reaction of the soil is directed downward so that a relatively undisturbed ap- SOIL DYNAMICS IN TILLAGE AND TRACTION 331

~~CGMMUNICATKDN "^ WIRE~~

~~(A) (B)~~

FIGURE 232.—Soil reaction resulting from the use of a chisel operated : A, With a small approach angle; and B, with a trailing approach angle. pearance results. Unfortunately, when one attempts to operate the tool at an angle of 132°, a very large force is required to draw the tool through the soil. Table 41 shows the influence of the angle of approach of simple chisels on the draft force ( 332, 515 ). Since the desired soil reaction can be obtained only at the expense of greater energy, the problem becomes one of balancing the greater expense of tillage against landscape repairs that would otherwise be required. Performance may therefore be reduced to economic terms without a specific measurement of soil conditions. ^ , . The performance required of special tillage tools for placing irrigation or drainage pipes differs from that required of special tillage tools for placing communication wires. The stability of some soils is low, and mole drainage channels do not remain open. Lightweight liners help to keep channels open and prolong their useful life ( 132, 287, 288, m ). Janert ( 191 ) and Busch ( 56 ) have designed machines to install drain liners. Two of the most difficult performance requirements are to maintain a predetermined grade and to place

~~TABLE à^l,—Effect of the approach angle on the draft force of simple tillage tools in sandy loam soils~~

Tool Draft Depth Rake or Source lift angle force Type Width of operation Inches Inches Degrees Pounds Vertical blade 0.3 8 45 1,250 Zelenin 90 1,470 {515). 135 1,650 Tine 2 6 20 100 Payne and 48 177 Tanner 76 325 {332 ). 90 449 104 513 132 564 332 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the lines without any blocks in the channel. A diameter gage ( 57 ) has been developed to measure the size of installed channels so that the blocking aspect of the performance can be determined. The correct grade usually has to be attained while the tillage action is being completed. Attaining the proper grade and open channels usually outweighs draft requirements. Thus, again, the intended purpose or use for the soil, and hence the tillage, determines what should be considered m measuring performance. Difficulties in maintaining grade are associated with positioning and guiding the tool rather than with any soil dynamics limitations. 6.4.3.3 Separating Highly specialized tillage actions are required for separating root crops such as potatoes and sugar beets from soil. These actions include not only removing the plants from the soil but also removing soil that may stick to the crop and separating the crop from clods of soil. Separating soil and clods from crops may be classed as cleaning and IS often performed after the crop has been removed from the soil. Highly specialized equipment and techniques have been used to make the desired separations. Maack ( 284, 285 ) summarized 29 methods by which separations have been made. Tillage before harvesting and tillage action during harvesting can greatly affect the amount of required separation. For this reason, separation studies are often conducted in connection with tillage. While these studies are an essential part of the total use of a soil, they are not directly related to information concerned with manipulation of soil. Con- sequently, these studies will not be discussed ( 22, ^6, 152, 16^, 222, 379, Jf.15 ). Performance of tillage tools in harvesting root crops is based primarily on effectively separating the crop from the soil. Of secondary importance is the force required to move the tool. A quantitative measure of the effectiveness of separation is usually not needed and IS not made. As in other specialized tillage actions, either the root crop is harvested or it is not, so that a measured degree of harvesting IS not very helpful. The suitability of a harvesting technique could be investigated, perhaps, in terms of percentage of lifted, mangled, or damaged roots. Attempts have been made to lift a plant directly from soil without excavating or disturbing the soil to any great extent. The force required to lift a plant must overcome the strength of both the root and the soil. These two materials are stressed when a plant is pulled from soil; failure may occur in the plant, in the soil, or in both. Some information is available regarding the forces required to pull plants from soil {183). Hülst, Gohlich, and Sochting ( 189 ) have shown that the force required to vertically extract sugar beets varies considerably with soil type (fig. 233). Extraction is much easier in wet soil than in hard dry soil. In dry soils the relative strength of the root and the soil becomes important because of possible damage to the root during extraction. To prevent damage, the extraction force has been reduced by partially excavating the root ( 189, 255 ). The partial excavation also entails severing certain lateral roots that bind the main root to the soil. As shown in figure 234, a steeply SOIL DYNAMICS IN TILLAGE AND TRACTION 333

~~110 LOAMY CLAY 100 HEAVY CLAY 90 HUMIC LOAM~~

~~^ 70~~

~~uj 60 SAND o g 50 11. 40 o z 30~~

~~t 20~~

~~O 6 8 10 12 14 16 18 20 22 24 26 ROOT LENGTH (cm)~~

FIGURE 233.—Effect of soil type on the force required to vertically extract sugar beets from soil. (Hülst, Gohlich, and Sochting, Zucker {189).) inclined lifter disturbs more soil around a sugar beet and therefore may decrease breakage of the beet. If a significant portion of the beet is left in the soil, the method becomes economically impractical. A wide angle between the lifting blades was reported to leave enough soil in front of the beet so that soil resistance prevented the beet from bending and breaking during extraction. The energy requirements of a steeper lifter may be greater, but a more effective extraction could justify the increased expenditure of energy.

~~V-/7777777.~~

~~(A)~~

FIGURE 234.—Partial excavation and Ufting of roots. (Hülst, Gohlich, and Sochting, Zucker ( 189 ).) 334 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE 6.5 Evaluating Performance To evaluate the performance of a tillage tool, the desired performance as well as the actual performance must be known. The desired performance and the actual performance are completely independent of each other, a fact that should be clearly kept in mind. Actual performance is controlled and determined by initial soil conditions, tool shape, and manner of tool movement. Desired performance is completely controlled and determined by the intended use of the tilled soil. Economic and other aspects associated with the intended use may temper the acceptable level of desired performance. The only relation between desired and actual performance is that the ratio of the two is an evaluation of performance ; when the desired performance is attained, the ratio is one. The most complicating factor in evaluation is that no unique relation exists between forces applied to a tool and the resulting soil conditions. Eotary and drawn tools may produce the same soil condition, yet different forces are required to operate them. Or two drawn tools may require the same forces, yet produce different soil conditions. As a result, no common denominator exists on which to base a comparison of tillage tools. The use of energy concepts may help to overcome this difficulty. The desired performance determines the level that should be attained m actual performance. As indicated in section 6.1, descriptions of soil conditions are determined by the intended use of the soil. Desired and actual soil conditions must be represented by the same numerical quantities if they are to be compared. Performance also includes tool factors such as the rate of performing tillage or the capacity of a tillage machine. Tillage machine capacity, when expressed m terms of miles per hour, acres per hour, or cubic feet per hour, IS not directly represented in the soil-machine mechanics or in the design equations. But the capacity of a tool is fixed for a given manner of operation ; hence, capacity is a useful measure of productivity. Expressions of desired performance generally include other factors of interest. Mechanical efficiency or power requirements are frequently incorporated into expressions of performance. Quantita- tive expressions of desired and actual performance must be stated m compatible terms to permit valid comparisons. Compatability is particularly hard to achieve when different tillage machines requiring different expressions for characterization are to be evaluated. The performance factor provides a concept by which compatability can be achieved. A performance factor is a term used to express the composite effect of measures of performance. A suitable performance factor for a drawn tool might be the change in soil conditions divided by the draft. The expression may be interpreted as an assessment of tillage efficiency. This performance factor can be combined with other performance factors, such as the capacity of the tool to do work, to obtain a different performance factor. Maximizing the product of a capacity factor and the performance factor that assesses efficiency would be one possible-optimum expression of performance that would have a significant meaning. If capacity were judged to be more important than efficiency—for example, because of the cost of labor— SOIL DYNAMICS IN TILLAGE AND TRACTION 335 the two factors could be weighted in the combined term. This concept has no limitations as to what constitutes a performance factor other than that the factor can be interpreted in a meaningful manner. Obviously, extreme care has to be used in devising a performance factor so that its physical significance is clear. Performance factors are often necessary when no clear-cut performance measure can be made, and they can be extremely useful in developing terms that can be evaluated. Maximizing or optimizing a performance factor does not indicate whether the performance is acceptable or even desirable. That decision can be made only by evaluating the performance factor. The difference between the numerical values of actual and desired performance evaluates performance. If the values differ widely, the performance may be judged to be poor even though the particular factor may be maximum for the situation. The complete independence of performance and evaluation of that performance must be recognized in order to fully utilize the concept. The concept of evaluating performance by comparing desired and actual performance is simple and direct. Unfortunately, desired performance cannot always be expressed in meaningful, finite terms. For example, the capacity of a tillage machine is usually desired to be as high as possible ; only in unusual circumstances will a definite capacity be desired. Similarly, the power requirements of a tillage machine are usually desired to be as low as possible. Since an increase in the capacity of a tool can be secured only with an increase in power requirements, a practical balance between the two factors must be attained. One means of overcoming the limitation in evaluation when desired performance does not have a fixed value is by using an evaluation factor. The evaluation factor is an extension of the concept of the performance factor. An evaluation factor is a term used to express the composite effect of individual performance factors. Eval- uation factors must be devised so that meaningful interpretations can be made; this requirement for interpretation is the only rule that guides or limits the development of a specific evaluation factor. The following general guidelines can facilitate the development of an evaluation factor. Each available fixed value of desired performance should be used as a separate term in the evaluation factor. Each term can be the desired performance divided by (the desired performance plus the absolute value of the difference between the desired performance and the actual performance). This technique produces a term that has a maximum value of 1 when the desired performance and the actual performance are equal. The term approaches a value of zero as the difference between the actual performance and the measured performance approaches infinity. If several such terms can be devised, the product of the terms would provide a meaningful evaluation factor. A value of 1 indicates that all actual and desired performance factors are equal and that the desired performance was attained. A value of less than 1 indicates that the desired performance was not attained by one or more of the individual performance factors measured. When individual performance terms are not of equal importance, they can be weighted to 336 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE reflect their relative importance. Weighting depends on a knowledge and judgment of factors other than performance. Consequently, a subjective judgment is required to assign the weighting factors. A second guide may be used when no fixed value can be assigned to desired performance. In such situations either a maximum or a minimum value of a performance factor is desired. If a maximum is desired, the performance factor can be one complete term of the evaluation factor. If a minimum is desired, the reciprocal of the performance factor can be a term. The combining technique permits development of an evaluation factor as the product of individual terms. When the evaluation factor includes either the performance factor or its reciprocal, the numerical scale of the evaluation factor IS determined by the units used in expressing the performance factor. Care must he taken that only evaluation factors having like units be compared. More desirable performance is indicated by larger values of the performance factor. Weighting the individual factors may also be required when either the performance factor or its reciprocal IS used. By using these two guides evaluation factors that facilitate the interpretation of performance of tillage tools can be developed. The concepts employed in evaluation are illustrated in the following example: The performance of three tillage implements (fig. 235) was measured during their operation in a firm clay soil; the efficiency of soil breakup was determined by using the drop shatter and sieving technique described in section 3.3.1 ; draft, torque, speed, and depth of operation were measured. These data are summarized in table 42; any data reported in the separate columns can be considered a performance factor. The desired level of performance was based on the following requirements : 1. Tillage must reduce clods to the desired size. 2 The energy applied to the soil by the tool must be efficiently utilized in breaking up the soil. 3. The power requirements per unit of soil tilled must be low. 4. The capacity of the machine must be high. Each requirement can be assessed by one or more of the performance factors listed in table 42. Clod size assesses the first requirement. The efficiency of soil breakup based on the drop-shatter energy assesses the second requirement. The product of forward speed and input energy per cubic foot of soil assesses the third requirement. The capacity of the tool, as expressed in terms of acres per hour, assesses the last requirement. To evaluate the overall performance, arbitrary values of performance to be attained by the tillage must be selected as the basis for comparisons. Clod size is the only term that can be expressed in a smgle^ definite value of desired performance; the three remaining quantities must be incorporated into the evaluation factor in the form of maxima or minima. Any one term can be taken out of the evaluation factor and plotted against the remaining terms to provide an evaluation relation. In the example being considered, the capacity term was isolated for this purpose. Three terms remain in the evaluation factor, and they were assumed to be of equal importance. When the first clod size (0.69 inch) is selected from table 42, SOIL DYNAMICS IN TILLAGE AND TRACTION 337

~~FIGURE 235.—Three types of tillage implements: A, Spading machine; B, conventional moldboard plow; and C, vertically rotating plow. (Thotograph B, courtesy of International Harvester Company.)~~

clod size can be evaluated for an assumed desired size of 1 inch by the computation LOO 1.00+11.00-0.69 I' Since power is to be a minimum and efficiency a maximum, and clod size can be compared with a desired value, the evaluation factor is the product of tlie clod size factor, tlie efficiency, and the reciprocal of 338 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~fe ^ J::^ r^ ^'^ (M lO o rH o (N 00 00 í^ O~~

Tfi Tt^ ÍO b- (N ÇOTHTHrHC^_ OOrHrH Ci Oi 00 (M (M Ö TA Oi (M* CO rH (TÍ (M*

~~fO ÇDTt^CO00t^ OOOOO 05 05 t- O 00 ■^ iO 00 rH r-l CO t^ CO CO OOOrH rH ^- rHOib-l>rí^ t-t-t> O O rH Ci 05~~

~~iO O O 00 lO O O lO »OOOOO »O C l> lO CD g (Xi CO b- O ^ 05 TÎ< CD (Tî CO CO (M 05 "^05 (M^ CO rH 05^ CO '^ Ö f^ 4J "•^' •"• a> 0) o ^ c6 oi (M" c~~

~~r-> rO iO p lO o lO »o o o OOOOO c^ t- CO 00 ^ CO rH CO 00 t^ lO 00 CO '^^ '^ '^ ^^ "^ CO o^co i> CO CO^ K5 t^ »O TîT TiT ïo Ttn" co'~(ríoíoí(M"~~

~~OOOOO TtH 00 CO T+( (M CO^ rH o 00 05 iO Tfl Tt^ »o Tfl CO'cîC^'^rH rH~~

~~íís o o OOOOO c^ o i> o t> CO rH CO -" 05 00~~

~~^ lOCOOOO ooo t-O O O O <^ C000CM^COO5 COCOTf t> lO CO rH 00 *¿ Ö ' rH TH rH CO CO 05 * rH (M' CO CO '?~~

~~rH CM 05 05 CO 05 00 TH TfH CO CM iO CO 05 rH O TH CM Tt^ CO Ö ' • 'rH~~

afcJD ^ Co n3 o KÎ Q, Pi ^ o P< m 1^ tí SOIL DYNAMICS IN TILLAGE AND TRACTION 339 the power requirements. These computations were made on the data in table 42 for three hypothetical cases in which desired clod sizes of 14, 1, and 2 inches were selected. The evaluation plotted as a function of the tool capacity factor is shown for the three implements in figure 236.

~~DESIRED MEAN WEIGHT DIAMETER .5 IN. 1.0 IN. 2.0 IN.~~

~~o 2 z o I-< z> /V~~

~~(A) (C)~~

~~J. _L. -L. J 0.001 L. -L- -I L- -L. 0.2 0.4 0.6 0.8 1.0 1.2 0 0.2 0.4 0.6 0.8 1.0 1.2 0 0.2 0.4 0.6 0.8 10 1.2~~

~~CAPACITY (ACRES/HOUR)~~

FIGURE 236.—Evaluation of the performance of three types of tillage implements at various capacities of work for desired clod sizes of %, 1, and Z inches mean weight diameter: A, Spading machine; B, moldboard plow; 0, a vertically rotating plow. The performance and evaluation factors used in this illustration should not be considered as the only ones or even the best ones for evaluating tillage tools. The factors are suggested as a means tor implementing the concept that performance and evaluation are two separate entities. They also illustrate the factors that can be developed from general principles which reflect the intent of the evaluator. New performance factors can be developed and tillage implements evaluated more precisely as soil conditions can be more accurately assessed. Until better definitions of the forces and soil conditions are available, evaluation will have to remain highly subjective and often comparative. 7. MECHANICS OF TRACTION AND TRANSPORT

7.1 Introduction Traction may be defined as the force derived from the interaction between a device and a medium that can be used to facilitate a desired motion over the medium. The usual traction device converts rotary motion derived from an engine into useful linear motion. Anchor devices such as winch sprags are exceptions to the usual concept, but they are traction devices since they provide traction by interacting with a medium—usually soil. Although the basic soil reactions are similar, the continuous rolling action of a wheel or track requires a different analysis than the stationary action of a sprag. The traction and transport devices considered here operate off the road and are construed to be wheels and tracks—that is, parts of vehicles rather than complete vehicles such as tractors. The number of off-the-road vehicles is rapidly increasing for agriculture, military, and construction purposes. The total engine power available for conversion into useful pull is generally in excess of the traction capacity that can be developed between the traction device and the soil. In other words, the limitations of the vehicle in respect to off-the- road movement are usually the limitations of the traction device. Furthermore, the efficiency with which a traction device converts energy into pull is usually extremely poor when the device is operating on soil. Work at the National Tillage Machinery Laboratory shows that a pneumatic tire operating on a concrete surface has an average power efficiency of approximately 75 percent. The same tire operating on various soils has an average efficiency of less than 50 percent. Nebraska Tractor Test results indicate that pneumatic- tired tractors operating on concrete lose approximately 5 percent more in thermal efficiency when the useful work output is expended through the drawbar than when it is expended through the power takeoff. Obviously, loss in thermal efficiency on soil will be even greater. Based on this minimum loss in thermal efficiency, some 152 million gallons of gasoline valued at $42 million are lost anually because of the inefficiency of the pneumatic tire. There are soil conditions where adequate traction and satisfactory efficiency can be obtained ; but, because of economic, social, and political pressures, such tasks as pest control, crop harvests, and military, mining, and construction operations are performed on extremely poor soil conditions where adequate traction cannot be attained. With the exception of loose dry soils, volcanic ash, or sand, most of the adverse conditions are associated with wet soils. Some of the land conditions on which operations must be conducted are so extreme that entirely new principles of vehicle design may be required. 340 SOIL DYNAMICS IN TILLAGE AND TRACTION 34:1 Much military research has been concentrated on these extreme conditions. Amphibious vehicles (Swamp Buggy, Amphibious Jeep, Bare), low ground pressure vehicles (Weasel, Polecat, Kolligon) and airborne vehicles (Aeromobile) represent traction and transport designs that were developed to improve performance under adverse conditions. The expanded requirements of traction have increased research directed at solving the problems of traction. Of notable importance have been the efforts of the Army Mobility Eesearch Center (sec. 1.2.2) and the Land Locomotion Laboratory (sec. 1.2.3). The approach of these research agencies has been to evaluate the performance of the entire vehicle. Eecently, greater emphasis has been placed on the basic aspects of traction mechanics—that is, the interaction between a traction device, such as a wheel or track, and the soil. The broad aspects of their research programs have been published {35, 37, 488, 495 ). The formation of the International So- ciety for Terrain-Vehicle Systems indicates the interest in efforts to secure better traction. . The term soil trafBcability was developed in connection with off- the-road vehicles. Trafficability may be defined as the ease with which terrain may be traversed. In the broadest sense, it includes the inñuence of all features such as vegetation, soil conditions, or slopes and includes barriers such as chasms or rivers. In trafficability, the primary interest is in the movement of the vehicle over the soil with little regard for the soil conditions produced by the movement. In agricultural operations, however, the effect of the vehicle on the soil may be more important than the maximum traction capacity that can be developed. A traction device that develops the desired pull at high efficiency may not be useful for agricultural purposes if, in the process, the device compacts the soil or ruts it so severely that excessive erosion, mechanical impedance, lack of moisture, or poor aeration drastically curtails the subsequent growth of plants. A device with a much lower efficiency and lower drawbar pull may be more suitable if the soil conditions created by the passage of the vehicle do not adversely affect plant growth. ^ Trafficability, in the broad sense, is not considered here since it includes such things as vehicle morphology, vegetation, and driver skill, in addition to soil trafficability. Instead, a restricted concept of soil trafficability embracing a simplified, relatively root-and-rock- free soil on ñat terrain is used. Soil trafficability is, therefore,^ considered in the light of soil conditions where slipperiness, stickiness, sinkage, and general loss of traction will limit traction. Vehicle mobility and trafficability may express the same quantity since the soil is not trafficable unless the vehicle is mobile. 7.2 Mechanics of Traction Devices A solution of the traction problem—that is, obtaining adequate traction at a suitable speed in a practical manner and at a reasonable cost—lies in an understanding of (1) the manner m which stresses are applied to the soil and (2) the reaction of the soil to the applied stresses. The general nature of the knowledge that will be required to solve the problem is known so that a direction of approach may 342 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE be established. Just as a soil-tool mechanics can be outlined (ch. 4), SO a soil-traction mechanics can be outlined. To simplify and examine the problem, let us assume that a rigid wheel IS operating on a deformable soil. As the wheel is placed on the soil, sinkage occurs and a known deformation of the soil results. With accurate stress-strain relations and parameters to describe the dynamic properties of the soil, the boundary condition on strain (which must coincide with the shape of the wheel) and the boundary condition on stress (which must be equal to the weight on the wheel) can be imposed and a solution can be obtained. Torque can then be applied to rotate the wheel ; now, given the yield criteria for the soil and the new boundary condition on stress, the new problem can be solved. Thus, the stress-strain equations for the soil, the dynamic properties of the soil, the yield criteria for the soil, and a mathematical description of the geometry of the rigid wheel are all required to solve the traction problem; all of these factors must be considered simultaneously to obtain a realistic and accurate solution. Consider now what happens in the same situation if a flexible wheel such as a pneumatic tire replaces the rigid wheel. The geometry of the wheel is no longer constant in the contact area and stress- strain relations describing the deformation of the flexible tire must be solved simultaneously with the boundary conditions that exist in the mutual contact surface during dynamic operation. No satisfactory equations of this type are available for either the soil or flexible traction devices. Even if they were available, they would probably be so complex that a solution would be difficult; consequently, simplifying assumptions have been made to assist in solving practical problems. As a result, the practical solution of problems, even though based on theory, may have limited accuracy. 7.2.1 Nonrolling Traction Devices To obtain a traction mechanics, both the soil and the device can be assumed to act as rigid bodies. This assumption provides a basis for a convenient mathematical model, but it sacrifices considerations about what happens to the soil. The simplest rigid traction device model utilizes frictional resistance to obtain the traction force. As shown m figure 237, the frictional force between a device and the soil can be expressed in simple equation form as ^ = i^y, (153) where H - the force available for traction, ¡x — the coefficient of friction between the rigid device and the soil, F = the normal load on the device. This representation expresses traction in terms of one dynamic property /x and assumes that all of the traction force is developed at the boundary. The representation adequately describes traction capabilities m several slippery traction conditions (wet grass, saturated clay, ice). One complicating aspect in the use of frictional forces as a means of computing traction is that the coefficient of friction may change with a change in the normal load (figs. 105 and 106). Load transfer SOIL DYNAMICS IN TILLAGE AND TRACTION 343

V ^ä b FIGURE 237.—The traction force íT in a simple rigid body system as related to the normal force V when the traction force originates from friction. resulting from drawbar j)ull and from the torque reaction of the traction vehicle itself may significantly change the normal load at any specific point in the contact area. Thus, alterations in the normal load must be expected. Eegardless of the magnitude of the coefficient of friction, the limiting factor in traction where equation 153 applies is friction. The solution is very simple since the concept implies rigid body behavior. If the surface of the traction device is indented by sharp grains of soil or if adhesion occurs between the soil and the device, inter- locking may result. Under these circumstances, failure occurs not by sliding friction along the soil-device interface but rather by shear within the ground medium as shown in figure 238 (34,), When

FIGURE 238.—The formation of a soil body (facl)) under a simple traction device permits utUization of shear strength of the soil in developing traction. (Bekker, Land Locomotion Laboratory (34).) failure is due solely to friction, failure occurs along the line /-&. For a load 7, the force available for traction H can be increased until the angle of sliding friction is exceeded. The force that causes failure (sliding movement) is the maximum force that can be developed for traction for that situation. With the equipment shown in figure 239, the traction force that can be developed by simple traction devices can be determined for varying H/V ratios. In addition, Bekker observed through the glass side of the apparatus box an apparently rigid soil body that formed and adhered on the bottom of the device {fach in fig. 238). Under these conditions, failure occurred in the soil rather than at the soil-device interface so that traction resistance originated from cohesive as well as frictional components of soil strength. The shear pattern that developed in the soil at failure was considered analogous to the pattern that developed under an imagi- 344 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~///////////////////////~~

FIGURE 239.—A simultaneous loading device with which desired H/Y ratios can be controlled in the study of traction by simple devices. (Bekker, Land Locomotion Laboratory ( ^^ ). ) nary continuous footing. Although later studies have shown that the concept of the continuous footing is probably not entirely correct, the important point is that a different type of failure occurs and that more than frictional resistance is involved. The failure surface is within the soil itself, and a logical assumption on which to predict failure is the Coulomb relation (equation 18). Bekker ( 35 ) reports that this approach was proposed by Micklethwait in 1944 where the relation has the form H = AC+Vtanct}, (154) where A = area of contact, V = normal load, O = cohesion of soil, (f) = angle of internal friction of soil. The possibility of causing failure deeper in the soil where a greater traction force can be developed suggests the use of lugs or grousers on traction devices. Breaking through a thin surface with a sharpened grouser where /x is the limiting factor may permit the device to engage soil with a greater strength so that failure occurs at a higher value of H. A different situation occurs when rubber tires are operated on rough concrete. The concrete may penetrate into the rubber and cause the rubber to fail as it is cut or ground off the tire. For the successful use of both equations 153 and 154, the traction device and the medium are assumed to behave as separate rigid bodies. SOIL DYNAMICS IN TILLAGE AND TRACTION 345

7.2.2 Rolling Traction Devices Equations 153 and 154 serve only to predict the maximum value for the traction force R, In reality, Z? is a function not only of the vertical load Y and the dynamic properties of the soil, but also of the displacement between the device and the soil. In assuming rigid body behavior, the flat plate or a combination of the plate and an attached rigid mass of soil (fig. 238) moves in relation to the larger mass of the ground medium. Figure 240 shows ^^-displacement

~~-CRACKS APPEAR SURFACE MOVES~~

~~SAND~~

~~.03 .04 .05 .06 .08 .09 DISPLACEMENT (In)~~

~~-CRACKS APPEAR~~

~~DISPLACEMENT~~

~~FIGURE 240.—S^-displacement curves in two media. (Bekker, Land Locomo- tion Laboratory ( ^4 )•)~~

curves for a constant Y in two media. The limiting values for B as given by equations 153 and 154 predict the highest values of K shown by the fi^-displacement curves. In nonrolling devices the value of H at any displacement may be easily determined, since the displacement distribution between the device and the soil is uniform. Thus, if the leading edge of a rigid plate moves 1 inch in relation to the ground, so must all other points on the plate. In a rolling device, however, the displacement distribution between the device and the soil is not uniform. The actual displacement is a function of the slip that occurs between the traction device and the soil and the length of contact between the device and the soil. Let us examine this point by considering the familiar form of an endless track, as shown in figure 241. The vehicle has a fixed co- 346 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Y'i

~~FIGURE 241.—The respective coordinate reference systems of a vehicle composed of an idealized rolling track.~~

Ordinate system (vehicle system) designated by a?'/. This vehicle coordinate system is moving at a velocity v with respect to a fixed earth coordinate system (earth system) designated by xy. Point Ä on the track has some velocity in the earth system, depending on the amount of slip between the track and the soil ; but at zero slip, by definition point A will have zero velocity in the earth system. In the vehicle system, however, point A has some finite velocity Vo that IS determined by the rate of angular rotation of the driving sprocket. Thus, for a constant angular rotation at zero slip, point A will have zero velocity in the earth system but will have velocity Vo in the vehicle system; consequently, the vehicle system must also have velocity Vo in the earth system at zero slip. At any positive finite slip, the velocity of the vehicle system v will be less than Vo. At 100-percent slip, the velocity of the vehicle system (v) will be zero with respect to the earth system (xy). Point A on the track will still have velocity Vo in the vehicle system and will also have velocity Vo in the earth system (xy). Slip is generally expressed as the ratio of decreased velocity to the initial velocity by

Vo ' where v = velocity of the vehicle system, Vo = initial velocity, S = slip, and by rearranging terms, V = Vo (l-S), (155) Equation 155 gives the velocity of the vehicle system—that is, the vehicle velocity—with respect to the earth system in terms of an initial velocity and slip. Using a unit vector i in the positive direction along the x and x' axes, the velocity of point A in the vehicle system is and the velocity of the vehicle system in the earth system is vi = Vo (l-S) i (156) SOIL DYNAMICS IN TILLAGE AND TRACTION 347 These quantities can be combined to determine the velocity of point A in the earth system, and this velocity is designated Va.^ From the laws of moving reference frames, the velocity of point A in the earth system is the vector sum of Vo i and v i. Since the unit vectors are in the same direction Vai = -Voi + Vo{l-S)i = -SVoi. (157) While equation 157 appears obvious from the definition of slip, the fact that two reference systems are involved, one moving in relation to the other, must be taken into account. In the earth system, by definition

~~^ = va^ -Svo. (158)~~

~~If point A is Sit X = Xo at time t = (9, equation 158 can be integrated between the appropriate limits giving~~

dx — — Svo dL Jxo Jo or ^x = x-Xo = - Svot, (159) where t^x — the actual displacement of point A in the earth system during time t.. In the vehicle system, point A is at some point x\ at time t = 0 and point A is at some other point x' at time t - t. If Z is a measure of the distance between x'o and x\ then, since point A has velocity Vo^ the time required for point A to move distance L is

~~By neglecting the effects of special relativity, time is the same in both reference systems so that~~

~~^x= -Svo— = -SL. (160)~~

Equation 160 thus gives the displacement of point A in the earth system with respect to a distance measured in the vehicle system and slip. Eecall that the objective of the analysis was to determme the distribution of displacements in the mutual contact surface of the rolling track and soil. The distribution of displacement in the vehicle system provides the desired information since it depicts the instantaneous situation in the earth system. No distribution of displacement is seen in the earth system after passage of the device; only the total displacement is evident. A distribution does occur m the contact surface but this surface is moving. Expressing the distribution in the moving vehicle system thus is a simple way to represent the situation. For a given slip, displacement starts from the point where the track and soil first come in contact and increases 348 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE along the track while it is in contact with the soil. Distance L should, therefore, be measured from the point of initial contact. Equation 160 will give the relative displacement at any distance L from the point of initial contact. The equation thus implies that the displacement for a given slip is zero at the point of initial contact and increases linearly to a maximum at the trailing edge of the mutual contact surface. A similar analysis can be made with the same results for other rolling devices such as a wheel; thus, equation 160 can be used to calculate the displacement at any point in the contact surface between a device and a medium. The exact location and amount of movement of the soil may not coincide with the relative movement of the device as represented by the displacement of point A in the earth system in the foregoing discussion. For example, if the relative movement occurs in a surface immediately adjacent to the device, no soil movement may occur. A form of grip failure is then said to exist, and equation 153 describes the behavior. On the other hand, some of the soil may adhere to the device because of a large coefficient of friction or because of grousers so that the movement occurs within the soil mass, and equation 154 approximates the situation. Equation 160 does not indicate where the relative movement occurs. Additional information is required to indicate which type of failure is involved or perhaps even some intermediate type of failure. As long as rigid body behavior must be assumed, only the relative movement between two reference systems can be described. An obvious complication for a traction theory for a rolling device thus is that even for uniform distribution of F, a nonuniform distribution of H is present because of the varying displacement. The first attempt to handle this problem was to ignore it. Micklethwait's equation 154 applied to tracked vehicles, and it was considered to give the maxinium horizontal force obtainable. The oversimplification does not give suitable results because it assumes a uniform normal load under the device and because it ignores the behavior of failure, as depicted in figure 239. The ^^-displacement curves and equation 160 imply that a rolling traction device must slip in order to

FIGURE 242.—The soil-vehicle geometry of an idealized tracked vehicle operating in a compactable soil. SOIL DYNAMICS IN TILLAGE AND TRACTION 349 obtain a traction force. Such behavior has been observed in measurements on actual traction devices. The general problem can be solved by determining the stress acting between the device and the soil at each point along the device and by summing the stress over the area on which it acts. Bekker ( SJf, ) reviewed how Gamalski outlined a graphical-analytical method for determining the traction force under a rolling track as a function of slip. With slight modifications, which better illustrate the principles involved, the method is as follows : Figure 242 shows a hypothetical tracked vehicle in operation. By using the soil values proposed by Bekker (sec. 3.2.2.2) and the Bernstein sinkage equation 51 P^ = KzJ" the vertical pressure can be equated to the vertical load so that

Y = 2& I Pdx = 2bK I ^oTdx, (161) Jo Jo where i = track width, L = track length. Pa; = pressure at point x^ Za, — sinkage at point x. Because of the existing relation between sinkage and track length ^x X or a. - [-j-y ^0 L By substitution, equation 161 becomes

V = 2bK \ i-^] dx = Jo \L ) ""^ n + 1 and solving for s„ gives [ yiiLi^r" (162) With So known from equation 162 and using the Bernstein equation along with the relation between z¡c and Zo we can write = K{^): (163) which provides a relation between the distance along the track and vertical pressure in terms of the vehicle parameters F, 6, and L and dynamic soil parameters K and n. Figure 243, A shows such a pressure distribution where n is less than 1. The average vertical pressure on each quarter section of the track can be used with the Cou- lomb relation shown in figure 243, B to determine the maximum stress that could be attained by the midpoint of each track section. Since not all points along each track section have been displaced enough so that the maximum stress is attained, stress H versus displacement j curves must be used to determine the average stress developed for each section. These relations can be conveniently measured for loadings that correspond to the average normal load under each track section (fig. 243 A) or be interpolated from a family of curves 350 AGRICULTURE HANDBOOK 316, U.S. DEPT. OP AGRICULTURE

~~P (p»i) (A) lr>^1 I I I ■ ■ ■ (D) J~~

FIGURE 243.—Graphic determination of the traction force of a tracked vehicle : A, The hypothetical distribution of normal pressure under the track; B, shear stress versus normal load relations for the soil; G, shear stress H versus displacement relations for the average normal load found in each section of the track; D, íT-displacement curves for different track sections. that bracket the average normal loads. Figure 243, 0 shows such ¿^-displacement curves. These curves, and others for natural soils in the field, generally appear to have the shape of type B in figure 41. The curves representing average iï-displacement relations for each quarter section of the track are shown separately in figure 243, D. When the length of the track is known, equation 160 can be used to determine displacement at any point along the track. Thus, the portion of each ¿^-displacement curve between displacements at the beginning and end of the respective track sections can be determined for a given slip. Figure 243, D shows the appropriate sections of the ¿i'-displacement curves that have been computed for the four quarter sections of the track for slips of 10 and 15 percent. The shaded areas beneath the appropriate portions of the curves may be divided by the displacement range for each area to give the average stress developed by each section. Multiplying the average stress by the area of the track section over which it acts and then summing the individual track sections gives the total traction force for each magnitude of slip. By using a number of slip values, a complete slip-trac- SOIL DYNAMICS IK TILLAGE AND TRACTION 351 tion curve can be constructed for a given vehicle in a given soil condition. The foregoing procedures accomplish what must ultimately be done mathematically. The graphical analysis approximates the tangential stress distribution beneath the traction device by discontinuous distributions. To be correct, the distribution must be represented continuously so that an analytical correct summation by mathematical integration can be accomplished. Janosi ( 198 ) has extended the principle to a track and a wheel so that a rigorous solution can be obtained. The method may give erroneous results, however, if the equations representing soil behavior are incorrect. Thus, both the Bernstein and Coulomb equations may give erroneous results even though the mathematics is logical and rigorous. The method does, however, demonstrate the essential requirements of a traction mechanics for a rolling device. Until this point only methods of analysis that provide estimates of traction force available to facilitate motion have been considered. Not all of the traction force in a rolling device is available for useful work. Some energy is required to deform the soil—that is, to overcome the rolling resistance of the device. Thus, the net drawbar effort will be the difference between the traction force and the rolling resistance. Several attempts have been made to calculate rolling resistance, but no method seems satisfactory at present (1965). Eolling resistance has many visible forms : sinkage or compaction, drag on the sides of the device, and a buildup of soil in front of the device above the original soil level. Building of soil is often termed bulldozing. These complex forms of rolling resistance are difficult to represent by mathematical models, which partly explains the inability to calculate resistance. When further considering that the forces involved in rolling resistance occur in the same area as the traction forces, it must be recognized that the traction devices do not distinguish between traction forces and rolling resistance forces; rather, the devices sense one distribution of forces. The concept of two separate force systems is thus useful for understanding and for- mulating the problem, but probably does not represent the physical situation. Steinbruegge ( Ji.ll ) proposed a concept of ideal traction efficiency of soil that might provide a useful addition to a traction mechanics. The concept employs the basic stress-deformation data, which can be obtained from measurements of S'-displacement curves such as those shown in figure 240. Since no traction force H is available until some displacement occurs, no traction force is available until some work has been done on the soil. The area under the ¿f-displacement curve represents work that has been done on the soil since a force H was moved through a distance j—the displacement. Figure 24e3, D shows the average work that would be done by each quarter section of a track operating at a given slip in the assumed soil condition. The area under an ^^'-displacement curve is not the only work done on the soil since, as sinkage occurs, the product of vertical force and vertical displacement also represents work. Stein- bruegge's concept is to maximize the ratio of traction force developed to the total energy lost—that is, the work done on the soil. This 352 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE maximum he termed the ideal efficiency of the soil. Figure 244 shows a method by which to determine the ratio. If a unit area supporting a vertical load Vi is placed on the soil in a given physical condition, some initial sinkage probably would

~~100%~~

~~IDEAL TRACTIVE EFFICIENCY~~

~~0%— TOTAL ENERGY LOSS~~

FIGURE 244.—The ideal traction eflaciency of the soil as determined from the energy lost in deformation. ( Steinbruegge, 1st Internatl. Conf. Meeh. Soil- Vehicle Systems ( ^ii ).) occur. The product of Vi and the sinkage represents work done so that some energy is lost even though no traction is yet available. As horizontal displacement is begun, a traction force becomes available while additional energy is lost from both vertical and horizontal displacement. For an infinite horizontal displacement, infinite energy is lost, yet the traction force remains finite so that the curve shown in figure 244 for load Vi has the shape indicated. If a second area loaded with V2 were used, the curve shown for V2 in figure 244 might result. Since a traction force available at no energy loss represents 100-percent efficiency and no traction force at any finite energy loss represents zero efficiency, a uniformly divided circular scale can be constructed, as indicated in figure 244. A line drawn through the origin and the point of tangency to a given curve defines the maximum S'-energy loss ratios for a particular vertical load on a soil. The intersection of the tangent line with the circular scale gives the ideal efficiency value. The most favorable ratio for the conditions represented is at the point of tangency. If the vertical load and horizontal displacement associated with the maximum ratio could be applied to the soil, use of the potential soil reaction should be optimum since the rolling device must supply the energy in order to obtain the traction force. If less horizontal displacement than the optimum is used, the traction force H will have a low value and the ratio will not be at the maximum value. Increasing displacement (increasing either slip or length of contact area) will increase the ratio. On the other hand, if more horizontal displacement than the optimum is used, energy loss increases faster than H so that the ratio is again less than the maxi- SOIL DYNAMICS IN TILLAGE AND TRACTION 353 mum. Steinbruegge concluded that the ideal efficiency gave the most effective loading of the soil to obtain traction. Obviously, an infinite number of possible loadings exists. A rolling device does not first apply the vertical load and then begin a horizontal displacement ; rather, the vertical load and horizontal displacement are simultaneously changed. Therefore, families of H- energy loss curves should be determined either at various constant vertical loads'or at various rates of increasing vertical loads. The maximum ratios attained by these families would represent the most suitable combinations of loadings and displacements for the given soil condition. From such information, a traction device designer could determine the combinations of normal loads and displacements that give the maximum ratio. As nearly as possible he could then design the length and size of contact area and the distribution of vertical load within the contact area to give the desired combinations. In other words, the device could be designed from the standpoint of the soil. The ideal efficiency concept can be generalized even further than indicated by Steinbruegge. He implied that the lost energy was absorbed by the soil; hence, the term ideal efficiency of soil. In reality, no assumption concerning the energy loss is necessary for the concept to be accurate. The unit area may be visualized as a rigid body; traction is obtained by the device thrusting against the area. That the unit area is physically a part of the traction device is not important. What is important is that the unit area moves both vertically and horizontally, that this movement reñects energy or work done on the unit area^ and that this work was necessary to obtain traction. The conservation of energy theorem states that the energy put into the unit area must be either stored or transferred. Steinbruegge considers the case where the energy goes into the soil. On ice, however, the energy can go into heat in the friction surface instead of permanently deforming the soil and the approach is still valid. Thus, in a generalized approach, the concept considers only the movement of the unit area necessary to obtain traction. Where the energy goes need not be considered. The device and medium are considered as two separate rigid bodies and their combined behavior as a system is described. The description might result in three- dimensional plots rather than two-dimensional plots, as shown in figure 244. For example, if H^ energy loss, and displacement were shown in three-dimensional space, a constant vertical load would describe some surface. The surface would represent the system behavior of the unit area represented (such as rubber, steel, or steel with grousers) and the medium. For a different vertical load, a different surface would probably result. Ultimately there must exist some envelope of all possible surfaces, and this envelope could be maximized for various effects. For example, maximum 5^-energy loss ratios could be determined for best efficiency of the medium or maximum ¿"-displacement ratios could be determined for minimum disturbance. Sinkage could replace displacement in the three-dimensional space to obtain ratios where sinkage is important. To maximize S'-energy loss, the circular scale could be retained as a cylindri- 354 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE cal surface or perhaps other statistical techniques could be used. Thus, by generalizing the ideal efficiency concept the behavior of a system composed of a traction device and medium could be optimized for a particular effect (maximum efficiency, minimum sinkage). The conditions reflected at the optimum would represent the best conditions at which to operate. Where some limitation restricts the range of possible vertical loads, the optimum within the restriction can be obtained. Where no limitation exists, the ultimate optimum (the envelope surface) can be obtained. The concept thus provides a method for obtaining information useful in design. While much effort is still required and many techniques still need to be developed before practical results can be obtained, the potential of the generalized ideal efficiency concept warrants the urgent efforts of future researchers. The assumption that rigid body behavior applies to both the soil and the traction device provides a basis for developing a traction mechanics. The assumption permits a development where stress- strain equations of the soil are not required since the forces and motions between the two bodies describe the desired behavior. While an assumption of rigid body behavior eliminates any possibility of describing behavior within the soil medium, it does adequately describe traction behavior. Thus, where only traction is to be considered, assumption of rigid body behavior is logical. Under such an assumption, a description of the forces acting between the rigid traction device and the rigid soil is adequate. For a given device in a given soil condition, the method of Gamal- ski ( Si ) demonstrated the principles of calculating the traction force. Steinbruegge's concept goes even farther; he proposed that an optimum loading can be determined for a given soil condition. A traction device can then be designed to provide as nearly as possible the desired loading for any situation. Ultimately, the methods could be extended to optimize the design for a group of different soil conditions. Attainment of these goals is not at hand, but is a challenge to the researcher. Accurate mathematical representations of the distributed forces between a traction device and a medium are required. A means of measuring ¿^-displacement curves that accurately represent the desired behavior or a means of calculating ZT-displacement curves from dynamic soil properties is required. Better methods for calculating rolling resistance are also required More accurate methods for determining energy loss in developing traction forces are needed. The attainment of these goals will provide a basis for a suitable traction mechanics. 7.2.3 Transport Devices A number of devices used to transport payloads over soil are not powered; they must be pulled. These devices range from rigid sliders such as sled runners to free-rolling wheels. The mechanics of these transport devices is not discussed here. Skids or runners operate by sliding, and the mechanics of sliding surfaces was discussed in section 4.3.1 The free-rolling wheel is a special case of the wheel in which the torque is zero. The forces on towed wheels are discussed later in this chapter (sec. 7.4.1.1). SOIL. DYNAMICS IN TILLAGE AND TRACTION 355 7.3 Characterizing Traction and Transport Devices Calculating the total traction and transport capabilities of a vehicle requires a knowledge of the forces that are transmitted through the mutual contract area between the vehicle and the soil. Without being restrictive, this contact area may include sites on the vehicle where lack of clearance above the soil causes drag resistance. Equations 154 and 162 can be used in estimating traction only when a representative value of the distribution of the horizontal and vertical forces is available. In the graphical-analytical method illustrated in figure 242 a hypothetical distribution of forces was used to solve the problem. At present (1965), such distributions cannot be accurately calculated, so it is necessary to determine them by experimental methods. Given these measurements it would be possible to verify equations that have been developed for computing traction and transport capabilities. In addition, it may be possible to identify more basic parameters that can be used to characterize the method of operation of these devices. Empirical correlations may then be made between characteristic distribution patterns and device performance or design variables used for constructing the devices. 7.3.1 Dynarnic Stress Distributions A number of techniques have been used to determine the stress distributions under statically and dynamically loaded traction devices ( U, ^S9, 394-396, 444, 498 ). The area of tire or track prints has been measured, and an average unit pressure has been computed from the total load. This simplification does not provide the distribution under the device that one normally assumes to exist. Attempts have also been made to measure the existing pressure distribution. In one method the pressure required to force air through small holes in a flat plate on which a tire was resting was used to indicate the contact pressure of the tire at each opening. In another method, small metal strips were placed beneath the loaded tire while it was standing on a flat plate. The force required to pull the strips from underneath the tire could be related to the normal load by means of the coefficient of friction of the strips. Depending on the location of the strips, the normal pressure could be estimated for various areas under the tire. Neither of these methods, however, actually indicates the dynamic stresses under the wheel while it is rolling since the magnitude and distribution differ for dynamic and static situations. In tracked vehicles, the load carried by the individual track shoes may differ at different points along the contact surface. Load may be transferred from the front to the back of the vehicle, because of the nature of the loading or because of irregularities in the terrain. Eogers and Tanner ( 372 ) measured the ground contact pressure by placing a stress transducer in the center of a track shoe (fig. 245). In order to register, the grouser or track shoe must be fully seated in the soil. A grouser plate fitted with a number of transducers of this type would provide a means for determining the distribution of stresses on the plate; however, this has not yet been done. Eeed ( 354, 355 ) used suspension links between the chain and the grouser plate in a bidirectional sensing unit (fig. 246). This unit is able 356 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~CANTILEVERi ^GAUGES~~

~~TRACK PLATE~~

~~FIGURE 245.—A simplified dynamometer developed to measure the contact pressure under a single track shoe. (Rogers and Tanner, NatL Inst. Agr. Engin. (372).)~~

FIGURE 246.—A track shoe dynamometer developed to separate the horizontal and vertical forces on an individual track shoe. (Reed, Amer. Soc. Agr. Engin. Trans. {355 ).) to measure the horizontal and vertical forces on an individual grouser plate during operation. Although nothing can be inferred about the stress distribution under the grouser, the total forces on the track can be determined. Figure 247 shows the vertical and horizontal forces simultaneously recorded during operation of the track in a clay soil. In a rigid track, the peak stresses noted on the vertical axis do not necessarily correlate with the location of the bogies of the track. Rather, fluc- tuations in the curves seem to be correlated with the vibrations induced by the driving sprocket rolling as a polygon rather than as a circle. Thus, it is possible to measure the influence of vehicle design factors—this is, the sprocket design—on the forces applied to SOIL DYNAMICS IN TILLAGE AND TRACTION 357

~~VERTICAL FORCE~~

~~HORIZONTAL FORCE~~

FIGURE 247.—Vertical and horizontal dynamometer traces as measured with a track shoe dynamometer. (Reed, Amer. Soc. Agr. Engin. Trans. {355).) the soil. This dynamometer has been used to determine the forces at all points of contact between a track of a vehicle and the soil (fig. 247). The force pattern applied to the soil may be determined from such information. One complicating factor is the direction of the applied forces. When the ground is hard, the track is horizontal and the orientation of the dynamometer is known. When sinkage or bending occurs, the orientation of the dynamometer in jiot known. Neverthe- less, the lack of similarity between measured forces and those envisioned in figure 243 indicates the pressing need for additional measurements.

~~AVERAGE VERTICAL PRESSURE~~

FIGURE 248.—Assumed average and measured distributions of pressure under a steel wheel. (Waterways Experiment Station ( 493 ).) 868 AGRICüLTURK HANDBOOK 316, U.S. DEPT. OF AGRICULTURE At the Waterways Experiment Station ( ^93 ) stress transducers were embedded in a rigid steel wheel so that the stress along the dynamic area of contact could be determined. Orientation of the ti'ansducers was fixed with respect to tlie position of the wheel. Thus, the location of the wheel could be associated witli the location and orientation of the transducers at all times. The distribution of stress under a rigid wheel operating in a clay soil is shown in figure 248. An assumed average vertical pressure may vary considerably from the measured vertical pressure; also the maximum pressure is found in front of the center of the wheel rather than below. In the rigid wheel, the pressure normal to its surface can be converted to a vertical pressure since the orientation of the transducer is known at all times. There seems to be a slight discrepancy between the total weight applied to the wheel and the weight computed from the vertical distribution. It is probable that tangential components also support the wheel and these components are not measured by this type of trans-

FiouRE 249.—Stress transducers embedded in tlie face of a tire to determine pressure in the contact area. (Vanden Berg and Gill, Amer. Soe. Agr. Engin. Trans. HGO ).) SOIL DYNAMICS IN TILLAGE AND TRACTION 359 ducer. Transducers that can measure tangential as well as normal pressures will have to be developed before this difficulty can be overcome. Stresses must be determined along the edges of the contact surfaces as well as along central portions. In spite of the need for simplified methods to determine stress distributions under traction devices, it must be concluded that realistic assumptions cannot be made until more actual data have been obtained ( 55, 178^ 4^6 ). The stress distributions between ñexible traction devices and the soil are more difficult to measure. The orientation of the transducer is rarely known when the wheel deforms ; therefore, the direction of the forces cannot be determined. Vanden Berg and Gill ( ^60 ) embedded transducers in the carcass of a smooth rubber tire in order to determine the stress pattern under a dynamically loaded wheel. Figure 249 shows the positions of the transducers in the tire along with other pressure transducers in the soil. Distributions were measured in both the soil and the tire. Pressure patterns obtained from transducers in the tire in several types of soil are shown in figure 250. The data indicate that the

~~^FRONT 12 6 REAR LENGTH (in)~~

~~FIGURE 250.—Pattern of pressure measured under the center of a smooth tire operating in several soil conditions. (Vanden Berg and Gill, Amer. Soc. Agr. Engin. Trans. {460 ).)~~

pressure pattern is influenced by the soil conditions as well as by the tire. Thus, this interaction must be studied. And in the absence of mathematical tools, the distributions must be experimentally determined. A complete vertical pressure distribution pattern can be constructed from a series of measurements made across the tire. The dynamic load on the wheel has been computed with an accuracy of 360 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE 5 to 10 percent by means of a graphic integration of measured data. Perhaps such pressure distribution patterns may be used to charac- tenze flexible tires. That the patterns may be radically different for different operating conditions is shown in figure 251 from data

~~I I I I 8 4 0 4 8 LENGTH (IN)~~

FIGURE 251.—Pressure distributions under a smooth 11-38 rubber tire on firm sand when inflated: A, To 14 p.s.i. ; B, to 10 p.s.i. ; C, to 6 p.s.i. The direction of travel was toward the right. (Vanden Berg and GiU, Amer. Soc. Agr. Engin. Trans. ( 460 ).) measured with transducers in the soil. Note that changes in inflation pressure alter the pressure distribution pattern considerably; also, the influence of sidewall stiffness becomes evident at the lower inflation pressures. Thus, the influence of design factors can be measured by stress distributions. Figure 252 shows the same distributions in three-dimensional models where large differences are readily apparent. Due to the rigidity of the tire carcass, the stress applied by the tire is generally greater than the internal tire pressure. When a very flexible tire SOIL DYNAMICS IN TILLAGE AND TRACTION 361

FIGURE 252.—Perspective three-dimensional views of pressure distribution under a smooth 11-38 tire on firm soil : A, Inflation pressure, 14 p.s.i. ; B, 10 p.s.i. ; C, 6 p.s.i. The direction of travel was toward the viewer. (Vanden Berg and Gill, Amer. Soc. Agr. Engin. Trans. ( 460 ).)

such as a low-ply low-inflation pressure tire is used, the pressure distribution is quite uniform. For some soil compaction research studies, this type of tire may be very useful because the inflation pressure is essentially the pressure applied to the soil. More complicated stress distributions occur under tires that have lugs. Unlike measurements on smooth tires, measurements at the contact surface on tires with lugs will probably have to be made on the device rather than from the soil surface. Trabbic, Lask, and Buchele ( 4<^1 ) have measured the contact stress patterns along the bottom, back, front, and on the carcass between the lugs of a tire on an agricultural tractor. The placement of the transducers is shown in figure 253. The measured patterns (fig. 253) are the maximum

~~0 6 75 13 5 O 6.75 13.5 0 6.75 13 5 WIDTH OF TIRE (in) WIDTH OF TIRE (in) WIDTH OF TIRE (in) (A) (B) (C)~~

FIGURE 2,53.—Effect of change in inflation pressure on contact pressures measured under a powered tractor tire ; A, On the carcass between the lugs ; B, on the face of the lugs; C, on the front of the lugs. (Trabbic, Lask, and Buchele, Agr. Engin. (iSl ).) 362 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE values at any location along the tire during one revolution. The patterns, therefore, do not indicate the instantaneous stress distributions that were presented in figure 251. The stress distributions along the surface of a traction device thus are complex and may vary continuously as soil and operating^ conditions vary. Hopefully, a better insight into the significance of these distributions will be obtained when improved instrumentation IS developed. Knowledge of the orientation, location, and movement of individual points along a tire will assist in providing parameters that can be of value in describing tires. The orientation of the stress transducers is usually not known when flexible tires are used. Better instrumentation, however, can help to overcome this difficulty. The same problem exists when transducers are placed in the soil and large soil deformations take place, since the transducers may rotate so that their orientation is no longer known. Corrections, however, have been applied to these position shifts {489), Transducers capable of measuring the tangential components of stress as well as the normal components must also be developed. Transducers will have to be constructed that will react more nearly like the surface of the material in which they are embedded. If the transducers are hard and rigid, they may cause stress concentrations; or, conversely, if they are soft, they may cause a bridging over the transducers. In either case, inaccurate measurements will result. In the past, because of the fragile nature of the sensing devices, measurements have been made only on slowly rolling, lightly loaded wheels. The strength and durability of these devices will have to be increased so that measurements can be made on flexible wheels having high torque inputs and high vertical loads. Both types of loading cause distortions and deflections in tires. Experimental evidence indicates that the distributions will differ not only for different soil conditions but also for different tires and for different degrees of wear on a given tire. In each case the distributions will have to be measured, after which generalized descriptions of stress distributions between the traction device and the soil may be made. The extent to which these descriptions can be placed in mathematical form will determine their value in contributing to a rigorous calculation of the traction capability of traction devices., 7.3.2 Deflections or Movements Between Devices and the Soil The distortion of pneumatic tires is one of the complicating factors in the study of their action on soil. Since flexing permits the tire to act as a nonrigid body, the direction in which stresses are applied and the size and shape of the area of contact may not be known. As a tire rolls over a surface, squirming or rubbing along the surface of the tire results from deformations within the tire. The importance of these movements on traction and wear of the tire has not been fully examined because the movements have not been completely measured. Several techniques have been developed for exploring these movements. Cegnar and Fausti ( 65 ) measured the movement of fixed points on a tire with optical equipment as the tire rolled over a flat surface. The actual movement or slippage of the lug at the center SOIL DYNAMICS IN TILLAGE AND TRACTION of the tire was as much as 4 millimeters, whereas at the edge of the tire it was as little as 1 millimeter. This differential movement of the lug has direct consequence in the loading of the soil since the soil is not brought to simultaneous failure all along the lug. Rollo ( 373 ) used a glass plate technique similar to that shown in figure 75 to study the movement in the horizontal plane behind lugs. No attempt has been made to use this method with a rolling flexible wheel where a differential movement of the lug occurs. AVann and Reed ( Jf70 ) have used a flat scratch plate technique without soil to determine the nature of creep under tires. (The differential movement of the tire in the contact area is defined as creep.) Photographic results (fig. 258) indicate that the movement patterns may be complex yet they may be indicative of design or operating factors. Bekker ( 36 ) has studied soil movement under grousers in the vertical plane by means of a glass-sided bin. While certain assumptions concerning the action of the soil against the glass must always be made, these techniques have provided an insight into the method of soil failure under traction devices. Since creep may do work on the soil in a direction other than the direction of travel, the energy efficiency of the device may be reduced. Attempts have been made to measure the gross differential slip to determine whether this factor influences traction performance {65). Wann and Reed ( 470 ) observed the net influence of this type of creep in the direction of travel by using a platform made of independent free-rolling parallel metal bars. Figure 254 shows the

~~FIGURE 254.—The differential slip of lateral sections of a rolling tire as measured by a sliding bar technique.~~

movement of bars 1 inch wide when a tire was rolled over the bars. Notice that the central section of the tire caused the bars to move forward while the exterior sections caused the bars to move rearward. Whether such measurements can be used to characterize the traction performance of tires has yet to be determined. External deflections recorded by scratch plates or other techniques 364 AGRICULTURE HANDBOOK 816, U.S. DEPT. OF AGRICULTURE do not indicate the amount of vertical or lateral movement within a tire. The Waterways Experiment Station ( ^84. ) has installed sensing gages inside tires to measure such deflections in dynamically operating conditions. Figure 255 indicates that the deflections vary

~~20 psi 40 psi 60 psi~~

~~_ '40» 40»~~

~~0« 0« 0«~~

~~VERTICAL CENTER LINE SECTION IN PLANE OF TIRE~~

~~VERTICAL CROSS SECTION OF TIRE~~

~~FIGURE 255.—Deformations in a flexible tire as influenced by tire pressure. (Waterways Experiment Station (^8^).)~~

at different locations in the carcass of the tire. Deformations of this type have been measured at vehicle speeds of 30 miles per hour, so it would appear that reliable instrumentation is now being developed for studies of this type. Additional measurements will ultimately be needed, since only two degrees of freedom are now being evaluated at the point of measurement. Whether the necessary measurements can be made easily depends in some degree on the miniaturization of the instruments, since they must be placed within the air space of the tire. Measurements such as these may be used to characterize flexible traction devices. Since tire design can influence these deformations, these measurements provide a practical link between the deformations and design. Performance, however, still has to be associated with the measured characteristics in some quantitative manner. 7.3.3 The Shape of the Contact Surface Knowledge of the shape and area of the contact surface between a device and the soil, coupled with knowledge of the stress distribution, provides a means of calculating the total forces in the mutual contact area. Measuring the shape of the contact area is difficult. A common method has been to ink the tread or body of the device and print the contact area on a flat sheet of paper. Since such a print represents static conditions only, its usefulness is limited. An SOIL DYNAMICS IN TILLAGE AND TRACTION 365 instantaneous contact area for dynamic conditions is the only accurate representation. To obtain a dynamic contact area, devices have been rolled through the soil and then stopped and lifted from the soil. This track may then be filled with plaster to reproduce the shape of the device when it was in contact with the soil ( 289, 290 ). Numerous tracer and grid measurements have also been utilized. The difficulty with these techniques is that the rut must be assumed to have the shape of the dynamically loaded wheel. Since pneumatic flexible devices try to re-form their original shape when they are unloaded, any decrease in the load on a tire causes it to move while it is still in contact with the soil. Thus, the pattern may be in error. One technique that overcomes this difficulty has been to place solidifying material inside the tire and maintain the deformation of the tire until it has set. At this time, even though the tire may try to re- form, the cast retains the distorted shape of the carcass. The stress and strain indicators described in previous sections may also be used to detect the point of contact of a tire. Stress transducers do not register until they are in contact with the surface. Correlating their registration with their position indicates the mutual contact surface. The orientation of the transducers must be known, or the shape and size of the contact area cannot be determined. With the internal deflection indicators, any deformation from the original undistorted position indicates a change in the shape of the tire. Knowledge that the change in shape occurs when the indicator is in the mutual contact surface is all that is needed to interpret the measurements. Enough measurements have been made to establish that a dynamically loaded contact area and a statically loaded contact area differ considerably in shape. In evaluating devices such as condual tires {21^6), information on the size and shape of the contact area is extremely important. Im- proved instrumentation and techniques will thus be required to accurately determine the shape and area of the contact surface between a device and soil. 7.4 Evaluating Traction Performance In section 7.2 it was pointed out that the distribution of stresses required to provide optimum traction could be determined from the stress-strain relations for soil and the dynamic properties of a soil in a particular condition. A traction device could then be designed to apply the desired stress distribution. The traction performance of the device would be near the maximum that is possible for that particular soil condition. The type of information required for this method of evaluation is not available at this time (1965). Were it available, the method would probably be too complicated for practical purposes. Even a mechanics based on rigid body behavior, some of which is available at this time, is not sufficiently advanced to be useful for evaluation. Evaluating traction performance is thus complicated because the performance of a given device, measured in a given traction condition, cannot be rated as good or bad based solely on methods that characterize the soil. In other words, the performance of a given device cannot be evalu- 366 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE ated in terms of a theoretical maximum performance in a manner similar to that of comparing the actual thermodynamic efficiency of a given engine with its theoretical maximum thermodynamic efficiency. Consequently, traction devices have, of necessity, been evaluated by comparing two devices under comparable operating conditions. 7.4.1 Criteria of Performance When comparing traction devices, the evaluation of performance is a subjective judgment that attempts to weigh the importance of the various desired actions of the traction devices. Certain criteria of performance must be selected to represent the actions, and physical quantities that can be used to represent these criteria must be measured. The first step in evaluating a traction device thus is to establish criteria of performance. The normal purpose of a traction device is to develop useful pull at some finite velocity. Usually, a minimum level of both pull and velocity can be established as a minimum satisfactory performance. The purpose of the vehicle on which the traction device is being utilized determines to a great extent this minimum performance and, hence, determines the criteria of performance. As an example, a military vehicle may only require a traction device capable of propelling the vehicle up a certain slope or across soils of poor trafficability. A tractor, on the other hand, may employ the same traction device, but the device must both propel the tractor and develop sufficient pull for draying. If the vehicle is to be used for extended periods of time, another consideration in performance is the mechanical efficiency of the system. Where unusual traction requirements are needed, such as for travel over loose snow or for minimum soil compaction during planting operations, some factor other than pull or efficiency may be the most important criterion of performance. In the final analysis such factors as durability, wear, and cost of manufacture must also be included in performance. Vehicle performance can be determined from a knowledge of the performance of individual traction and transport devices. Since vehicle design and requirements differ so greatly, only the traction device is considered here. Further- more, economy factors are not considered, and only performance concerning traction is discussed. 7.4.7.1. Drawbar Pull The forces that act on a rigid wheel operating on soil have been analyzed by Vanden Berg, Eeed, and Cooper ( ^62 ) for several special situations. The magnitudes of these forces are criteria of performance and the relations between the forces must be clearly understood. The forces that act on the soil and the wheel are typical of those found on any device where rotary energy is converted into translational energy in a continuous process. How- ever, only the forces acting on the wheel are shown. The vehicle applies forces to the wheel at the axle while the medium applies forces in the mutual contact surface—that is, the soil-wheel interface. The hypothetical distribution of forces acting on the wheel SOIL DYNAMICS IN TILLAGE AND TRACTION 367 may differ from those postulated for other traction devices but the same principles of equilibrium are involved. The scheme of forces shown in figure 256, A represents the wheel acting as a transport device rather than as a traction device—that is, the wheel is being towed over the soil. The forces in the contact surface between the wheel and the soil represent what might be

~~//////~~

~~/////~~

FIGURE 256.—Forces acting on a rigid wheel : A, Transport wheel ; B, traction device; C, traction device but forces are hypothetical forces of thrust and rolling resistance; D, traction device where the pull is zero. (Vanden Berg, Reed, and Cooper, 1st Internatl. Conf. Mech. Soil-Vehicle Systems Proc. (462).)

considered a reasonable distribution; the lengths of the vectors represent the magnitude of the envisioned forces. From equilibrium conditions, the pull P that is required to move the wheel must be equal in magnitude, but opposite in direction, to the sum of the horizontal components of all forces in the contact surface. Simi- larly, the sum of the vertical components of all forces must be equal in magnitude, but opposite in direction, to the total weight W. Ne- glecting friction, the moment at the axle is zero; since no tangential forces can exist, the line of action of all forces in the contact surface must pass through the axle. The resultant B of all forces 368 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE acting in the contact surfaces, therefore, has components P and TF, and must pass through the axle. The scheme of forces shown in figure 256, B depicts the wheel acting as a traction device—that is, it is developing pull. Kotary power 7a) is applied to the axle, and the output power that is developed is Pv where T is the torque, o) is the angular velocity, and V is the forward speed. From equilibrium conditions, when accelerations are assumed to be zero, the components of the resultant force R are again precisely P and W, The moment at the axle, on the other hand, is not zero ; R must therefore be so located that the relation T = Rl is satisfied. The torque arm I for the force R and its location is as indicated in figure 256, B, The concepts of thrust and rolling resistance have been based on the assumption that each acts as a force between the traction device and the medium ( S61, ^62 ). Figure 256, C shows a possible interpretation of this concept. All of the horizontal components of force acting in the direction of travel shown in figure 256, B can be summed, and their sum defined as thrust S. Similarly, the sum of all horizontal components of force acting opposite to the direction of travel can be defined as rolling resistance Ü. From equilibrium conditions, thrust is equal to rolling resistance plus pull. That physical quantities do exist seems logical when they are defined in this manner. However, measuring or calculating either thrust or rolling resistance is extremely difficult. The length of the lever arm—the distance below the axle—where either S or Ü acts is not known and is not easily determined {Jf62), Furthermore, the magnitude of neither S nor Ü can be calculated or measured ; only their difference P can be measured. -Because both thrust and rolling resistance occur in the same physical area, they are difficult to separate. Conse- quently, their hypothetical existence merely reflects a confusing model of the actual forces in the contact area. Great care should be exercised when the concepts of thrust and rolling resistance are used as criteria of performance. 7.4,1,2 Speed and Slip In addition to being able to develop an adequate drawbar pull, the traction device must be able to develop enough speed so that an adequate amount of work can be accomplished. Thus, speed is another criterion of performance and indicates the ability to travel a given distance in a given time. When no slip occurs between the traction device and the soil, the size and angular velocity of the wheel determine the velocity of the vehicle. Actually, because of the basic soil reaction, which is characterized by ZT-displacement curves (fig. 240), there will be relative movement between the traction device and the soil. Slip is a measure of the relative movement and it is related to velocity, as shown in equation 155. Slip is thus important in determining forward speed. Even more important, however, is a knowledge of the actual movement between a device and the soil since relative movement is directly related to the traction force available for reaction, as indicated by ^-displacement curves. Eelative movement itself is thus an important criterion of performance. Because of the great importance of the SOIL DYNAMICS IN TILLAGE AND TRACTION 369 relative movement between a device and soil, the ramifications of measuring the movement by slip are discussed in considerable detail. In section 7.2.2, an idealized track was analyzed and equation 160 was derived. The equation expresses the relation between slip and relative movement in the mutual contact surface between a device and a medium. Recall that equation 160 was derived from the movements of two coordinate systems—a vehicle system and an earth system. Point A was used to represent one particle on the surface of the track. Expressing the motion of point A m the vehicle system was easily accomplished for the idealized track. Based on the accurate representation of the motion of point A, a rigorous relation between slip and the relative movement of point A in the earth system was derived. To illustrate the validity, consider an idealized wheel rolling on a surface where rolling resistance is zero. By definition, zero slip occurs when point A is in the mutual contact surface and does not move horizontally in the earth system. When the instantaneous center of rotation of the idealized wheel lies exactly on the circumference of the wheel, the wheel rolls over the surface with no relative movement at the point of contact (267). Thus, the zero slip condition is satisfied; and, obviously, the motion of point A m the vehicle system is readily described from simple geometrical considerations. A similar argument can be made for the idealized track or any other device. Visualize what happens, however, if the wheel is flexible and deforms in the contact area or if the track stretches or bends between bogies. The motion of point A is no longer accurately represented by equation 157. With enough additional information available so that the velocity of point A could be accurately expressed m the vehicle system, equation 157 would become more complex but it would accurately reflect the velocity. The remainder of the derivation would proceed in the same manner, but equation 160 probably would have a different form. Eigid body behavior is not essential to the derivation, and stretching and flexing of devices can be handled by the mathematics. The crux of the accuracy ot equation 160 thus rests on the accuracy of representing the motion o± point A in the vehicle system. The path of motion of the surface of a real traction device is difficult to describe mathematically. This difficulty has led to the recognition of two phenomena involved with slip ( ^62 ). The two phenomena are associated with the two bases for defining slip. Equation 160 suggests that a ratio j/L can be used to define slip, and the fundamental quantity is the relative movement m the mutual contact surface—the movement of point A in the earth system. On the other hand, equation 155 can be used to define slip, but the fundamental quantity is the movement of the vehicle system—the movement of the origin of the vehicle system m the earth system. Both fundamental quantities are important. The first is involved in the ^-displacement phenomenon; the second, m the forward speed phenomenon. In an ideal traction device, both definitions o± slip will give the same magnitude for a given situation. But this is not necessarily the case in a real traction device because, as has 370 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE been pointed out, the motion of point A may not be accurately described in the vehicle system. In the real device, slip can and does differ for the two definitions. No practical method exists for measuring slip based on the definition involving relative movement. Measurement of the velocity of the vehicle system, however, is relatively straightforward ; hence, this definition is generally used. When the motion of point A cannot be described, the initial velocity Vo cannot be described. Thus, even this definition (based on vehicle motion) does not yield a straightforward measurement although the definition is straightforward in concept. The solution lies in an accurate description of the path of motion of point A. In the meantime, measurement of the movement of the vehicle system is used in slip measurements. The relative movement phenomenon is introduced in attempting to define a zero slip condition—that is, the motion of the vehicle system while no relative movement occurs in the contact surface. The problem of measuring slip thus becomes one of defining and measuring zero slip. For a flexible device such as a pneumatic tire, defining zero slip IS very difficult. Keed (356) measured the distance the axle of experimental tires moved forward in one revolution while the tires were operated at the self-propelled point on a hard surface. Figure 256, D shows the forces on a wheel while it is operated in the self-

~~1.5 l£ 17 1.8 \3 1.7 1.8 13 2J0 2.1 LENGTH (Ft) LENGTH (Ft)~~

FIGURE 257.—RoUing radius of four pneumatic 11-28 tires compared to axle height and undeflected radius : A, Smooth conventional-ply tire ; B, same tire with lugs; C, smooth radial-ply tire; D, same tire with lugs (After Reed Amer. Soc. Agr. Engin. Trans. ( 356 ). ) SOIL DYNAMICS IN TILLAGE AND TRACTION 371 propelled state. Data in figure 257 show that the rolling radius (the distance the axle moved forward divided by 2 TT) for the condition (2,0704b. load at 14 p.s.i. on concrete) was not uniquely related to either the axle height or the undeflected radius (no load on the tire). If the tires are operated in a soil where smkage occurs, a different rolling radius probably will be found at the self-propelled point. Quite clearly, no simple method exists for defining a theoretical rolling radius of pneumatic tires. . -...r The deformation of flexible traction devices takes place m diöer- ent directions {m), as illustrated in studies by Wann and Eeed ( IL70 ) The relative movement between the contact surface o± a tire and a hard surface was studied by a flat scratch plate technique. Carborundum particles were uniformly distributed over a polished aluminum plate after which a tire was loaded and towed over the surface. The carborundum particles scratched the surface ot the plate as they were moved by the scrubbing or squirming of the tire. A special red-base waxed paper was bonded to the surface ot the

FIGURE 258.—Scratches made by the movement of a conventional 11-28 tire on a flat plate: Left, 2,070-lb. load and 14 p.s.i. inflation pressure; right, 1,470-lb. load and 10 p.s.i. inflation pressure. (Wann and Reed, Amer. Soc. Agr. Engin. Trans. (^70 ).) 372 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE plate to record the scratches. Figure 258 shows the scratches produced by a tractor tire having two loads and inflation pressures. The paths along which the individual grains of carborundum moved show clearly that the direction is sidewards as well as rearwards in some mstances. In addition, the scratches reveal one part of the contact area may be operating at essentially zero slip while another part has slipped considerably. The following explanation for the action was given by Wann and Eeed {^70). The circular cross section of the tire can be considered to be made up of an infinite number of circles of varying circumference, which are constrained so as to rotate on one axle and operate as a unit. As a result, differential slip between the various circumferences and the surface must occur. To examine this action of tires, a bar table consisting of flat bars 1 inch wide operating on and between frictionless bearings was used. The bars were so supported that they were free to move lengthwise even though they were kept in alinement and restrained from lateral motions. The use of the bar table permitted the measurement of the cumulative relative movement in increments 1 inch wide as a tire traveled forward on the bars in a self-propelled state (fig. 254). Figure 259 shows the result of the measurements for several experimental tires. The data were expressed in terms of movement relative to the center line of the tire per unit distance of travel and show the same general effect indicated by the scratch tests. The complexity of defining zero slip for a flexible traction device becomes apparent in the light of the numerous movements indicated by the data just discussed. The problem is to define, the theoretical distance or velocity traveled at zero slip. Since no convenient method based on relative movement is available for describing zero slip, an alternate method is to describe the state of forces on the device. For example, in the theoretical wheel operating at zero slip, the torque and the pull are simultaneously zero. In the real wheel where rolling friction (rolling resistance) is present, torque and pull are never simultaneously zero. Phillips ( 335 ) suggested that three methods of operation exist on which a zero slip measurement might be based: (1) the distance traveled by the wheel in one revolution at zero torque; (2) the distance traveled in one revolution of the wheel in the self-propelled state; and (3) the distance traveled when the instantaneous center of rotation of the wheel is at the undisturbed surface of the medium on which the wheel is operating. All three methods of operation would predict the same rolling radius for a theoretical wheel if no sinkage occurred. When sinkage does occur, the third method does not seem to be logical since it results in predicting a rolling radius that is less than the actual radius of the wheel. Figure 260, A shows a deformable wheel operating in a medium where sinkage occurs and B^ on a medium where all of the deformation takes place within the wheel. Within the contact area, the radius of the wheel varies from R^ to Ro; however, the value R^ depends on the soil condition and the character of the wheel. The rolling radius should logically lie between these tw^o extremes. The data in figure 257, obtained with a self-propelled wheel having forces as depicted in figure 256, />, SOIL DYNAMICS IN TILLAGE AND TRACTION 373

~~liJ .03r~~

~~Xo er Lu CL~~

~~-.01 12 3 4 (^ DISTANCE FROM CENTER LINE (in)~~

FiGUBE 259.-Accumulated movement of bars relative to the center of the tire caused by differential movement of different sections of the tire: A, conven- tfonalDlv smooth tire; B, conventional-ply lugged tire; G, radial-ply smooth tiref I! rfSatply lugged tire. (Reed, National Tillage Machinery Labora- tory.)

~~'m^//À^/y (A) (B)~~

FIGURE 260.-Limits of rolling radius of a deformable wheel: A, Deformation in the tire and soil; B, deformation only in the tire. 374 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE clearly show that the measured rolling radius does lie between the two extremes Ri and Ro. An interesting observation concerning the data m figure 257 is that the rolling radius appears to be approximately halfway between the two extremes. Phillips' third method however, suggests a value for the rolling radius that is even less than Ro when smkage occurs. Thus the approach in which the instantaneous center of rotation is considered to be at the surface of the undisturbed soil can result in a rolling radius that does not lie between the extremes. The two choices that appear to be available for establishing a basis oí zero slip are the towed and self-propelled states. Until some different manner of specifying an accurate rolling radius can be developed, one of these two bases will have to be used. Most researchers have used the self-propelled state as a base, and a number of arguments can be made for using this approach. The net horizontal force in the contact area is zero. The self-propelled state IS also the transition point between a traction device and a transport device. This is to say, it represents the state where the traction device provides neither a pull nor a braking force. As a machine, its drawbar efficiency is zero at the self-propelled point since all input energy is lost in th^ contact area. The self-propelled state IS also rather clearly defined as a condition of operation. The one difficulty is that the definition is based on the state of forces and not on relative movement. Where the assumptions are applied m an extreme case, the result can be a situation not represented by the model. For example, when a device sinks deeply into sticky mud and is just capable of moving itself forward so that its net pull IS zero, the device will probably be spinning. The relative movement between the device and the mud will obviously not be that of a zero slip, and it is apparent that the defined condition ^^^ ^?} ^PP^^- Usually this extreme situation does not exist, and the self-propelled state provides a logical estimate of zero relative movement. All present definitions of slip are based on travel and the assumption IS then made that the net relative movement, in terms of displacement, can be calculated by using equation 161. Since the distance traveled at zero slip must generally be arbitrarily defined, no accurate measure of relative movement can be established until the actual displacement distribution in the contact surface can be expressed m terms of parameters that describe the surface and the device. Such a description must involve ih^ length of the surface and the geometry of the device so that the path of a theoretical point J. can be expressed mathematically. At present (1965), the self-propelled state seems to be the most logical basis on which to define zero slip and thus provide one of the more important criteria of performance. 7.4.7.3 Energy Efficiency The primary purpose of a traction device is to develop pull at a reasonable forward speed. When the device is operated for long periods of time, however, its efficiency of energy transfer becomes important. Power efficiency is, therefore, a criterion of traction performance. In reality, power efficiency is a specific combination SOIL DYNAMICS IN TILLAGE AND TRACTION 375 of the criteria discussed in section 7.4.1.1, namely, the forces that act on the device. Because the combination has a definite physical meaning, however, it is useful as a criterion. Energy transfer is usually expressed as a ratio of output power to input power. For a tractor pulling a load, the output power is the product of pull and forward speed, while input power is the product of torque and its rotational velocity. Within the range of speed of most off-the-road vehicles, traction performance is generally assumed to be independent of speed. A device can be operated at 10-percent slip at either 1 or 10 miles per hour with the same relative movement with the soil. The only difference in the action at these two speeds is the time during which the movement occurs. If two devices are required to develop a specific pull at a definite forward velocity, the rotational velocity (throttle setting) can be adjusted so that both pull and forward speed are at their desired values even though the devices may be slipping at different rates. Under these conditions, both devices may be visualized as black boxes doing the same work—that is, their output power is the same. The difference in the boxes, if any, is the input power required to operate them. Since forward speed can presumably be varied by varying rotational velocity, power efficiency expresses the efficiency of converting rotational power to translational power. Power efficiency is thus a meaningful criterion of traction performance. A clear understanding of power efficiency is necessary m order to properly use it as a criterion. In section 7.4.1.1, the concept of thrust was mentioned and the difficulty of determining the magnitude of thrust was pointed out. In the past, thrust was often assumed to act on a lever arm equal to the rolling radius of a wheel, an assumption that is true only for an ideal wheel operating where no sinkage occurs. On the basis of this assumption, however, a ratio (force ratio) of thrust to pull can be established. The concept of travel ratio (defined as the ratio of the distance actually traveled to the distance that would have been traveled if no slippage had occurred) was also used in the past. Power efficiency was then conceived to be the product of two factors—the force ratio and the travel ratio. One of the shortcomings of this approach is that power efficiency can never exceed the fraction of travel that was lost in slip. In other words, when the wheel slips 10 percent, only 90 percent of the total power is considered to be productive and the total power efficiency should never exceed 90 percent. In the physical system, however, power efficiency as calculated by the relation -^ (164)

frequently exceeds 90 percent when slip is in excess of 10 percent. The difficulty is that the energy lost in slipping the wheel cannot be determined. Power efficiency refers only to the ratio of total power output to total power input. That efficiency is composed of two factors is perhaps a confused concept, particularly since the magnitude of thrust cannot be accurately determined at this time. 376 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE The work that a given traction device can perform in a given traction condition is also a criterion of traction performance. Dickson ( 102 ) emphasized that the velocity at which pull is developed must be considered in addition to the magnitude of the pull. In many traction conditions maximum pull is reached at or near 100-percent slip, but the device may be moving forward so slowly that it is not a very practical device. Some measure that includes the influence of both pull and speed would therefore be useful. The coefficient of traction (pull divided by weight carried) multiplied by the travel ratio is one possible factor. For a constant rotational velocity, the factor has the form

TT^;;' (165) where Vt is the theoretical velocity, v is the actual velocity, and P and TF are the pull and weight on the device as indicated in figure 245. Both V and Vt are a function of rotational velocity co; and in equation 155, vt is the same as Vo for a constant w. Equation 165 can be made independent of rotational speed by substituting for V from equation 155, giving

^(1-^). (166) where 8 is slip. In equation 165, since the rotational velocity co can be maintained constant, the denominator (Wvt) will be constant. The numerator, however, >aries from zero at zero slip (since P is zero through a range of positive values) to zero at 100-percent slip (since v is zero). The units of the numerator are those of work so that the expression represents the work output of the device for certain fixed conditions (weight and rotational velocity). The expression thus may be called a work output, and it is an index that represents the work in dimensionless terms. Since the work output reaches a maximum, the pull associated with the maximum represents the pull at which maximum work can be performed. The denominator in equation 165 IS not work even though the term has the units of work. The vectors Vt and Tf operate at right angles to each other so that their product is not work in the normal sense even though a superficial inspection would so indicate. Because the work number in equations 165 and 166 represents work done, the number is a useful criterion of traction performance. 7.4.7.4 ioocf-carr/ing Capacity Transport performance may be evaluated in terms other than towing force and speed. For a self-propelled vehicle, the time required to move a specified distance could be a criterion of performance. With rare exceptions, however, the object of vehicular travel is to move a load rather than merely to deliver the operator from one place to another. Dickson ( 102 ) proposed a load-carrying index which was suited to a vehicle with a drawbar load ; a more general form might be SOIL DYNAMICS IN TILLAGE AND TRACTION 377

~~load carrying index = 7^^ +Vv ' ^^^"^"^~~

where Wp = payload, T — torque, CO = angular velocit}^, P = drawbar pull, V = velocity. For a self-propelled wheel, the pull term Pv would go to zero. The advantage of this form of load-carrying index is that it also applies to the transport wheel. In the latter, the torque term Tœ goes to zero and P is a minus quantity signifying a towing force. Wp would be the load transported on level soil. If the vehicle climbs a hill, the force parallel to the ground line will increase. The increase acts as additional drawbar pull P which causes a decrease m the load-carrying index when the vehicle operates on slopes ( ^/5 ). Load-carrying index is thus a useful criterion for evaluating transport. 7.4.2 Measures of Performance As indicated in section 7.4.1, the first step in evaluating traction performance is to establish fundamental criteria of performance. Since traction devices must be compared, the second step is to quantitatively measure the established criteria. The criteria can then be compared. For example, in one instance the most important criterion may be maximum pull, whereas in another instance it may be power efficiency. These fundamental criteria are not independent, as has already been indicated (sec. 7.4.1.1), but are interdependent in various complex relations. Furthermore, the relations depend on the state of operation of the device. Therefore, to establish these relations, the fundamental criteria must be simultaneously measured in various states of dynamic equilibrium. Eegardless of the fundamental criteria chosen for comparison, certain basic measurements are required. Pull, torque, weight carried, rate of angular rotation, forward speed, and slip are basic measurements that describe the state of dynamic equilibrium. Composite criteria such as power eificiency can be calculated from the fundamental criteria, bpecial equipment is generally required to control the operating conditions and to make the measurements. The equipment shown m figures 2 and 3 was designed for this purpose. Figure 261 shows traction measurement equipment at the National Tillage Machinery Labora- tory. The control and measurement of fundamental criteria with this type of equipment provides reliable information that can be used to evaluate traction performance. Traction depends on the relative displacement ot the traction device, as demonstrated by the ¿T-displacement curves shown m figure 240. Equation 160 shows the relation between slip and relative displacement for a rolling device; this relation was discussed in detail in section 7.4.1.2. Figure 262 shows typical traction data where torque and pull have been plotted against slip by using a self-propelled state as the zero slip condition. Data on traction 378 AGRICtLTURE HANDBOOK 316, U.S. DEPT. t)F AGRICULTURE

~~:SS¡BS^S^¿~~

~~FIGURE 261.—Traction measurement equipment at tlie National Tillage Ma- chinery Laboratory, Aul)urn. Ala.~~

~~- BRAKED DRIVEN -~~

FIGURE 2G2.—Torque input to a wheel and drawbar pull of a rollin}; device as affected by the slip between the device and the soil. (After Freitag, Au- burn Univ. ( ISi ).) measurements are usually obtained with a constant weight on the device when it is operated on a uniform ground medium. Depend- ing on the direction of the applied torque, the device is either braked or driven. Where torque is zero, tlie device is a transport device and the negative pidl represents the force required to tow the device in the medium with the carried weight. If the device is used on an all-member drive vehicle, tlie self-proi)elIed state represents the operating state where sufficient traction is available to overcome the rolling resistance of the soil and to propel the veliicle. When climbing a slope, however, the device must generate additional tractio^t in order to overcome a component of the weight along the direction of travel ( 37,1^75 ). The first quadrant of the axes shown SOIL DYNAMICS IN TILLAGE AND TRACTION 379 in figure 262 thus represents the operating states where the device is providing a draying force and hence is a traction device. As figure 262 shows, however, the device can be used for other purposes such as braking and the total information shown is useful and characteristic of both the device and the medium on which it is operated. n - j- Because of the mechanics of some types of equipment tor measuring traction, weight may be transferred to the traction device as drawbar pull is increased. Weight also varies with the slope of the ground. These weight changes must be measured and the traction results expressed in a form independent of the changes. Such a form is provided by the coefficient of traction, which is defined as the ratio of pull to the total weight carried. Use of the coefficient, however, requires the assumption that the coefficient is independent of the normal load. Quite clearly, such an assumption is not justified when large variations m the vertical load occur. For example, if a coefficient of traction-vertical load relation is visualized, the pull capability of the device reaches a finite maximum; and as the vertical load increases, the coefficient must approach zero. At the other extreme, in the limit, the coefficient becomes undefined since it approaches the ratio zero/zero; however, researchers ( lOß ) indicate that the coefficient approaches infinity as the vertical load approaches zero. Approaching infinity does not seem unreasonable; it merely indicates that the rate at which pull and vertical load approach zero are different and the rate of pull is slower. The important point is that the coefficient does not express the desired information, namely, the maximum pull for varying normal load; consequently, when trying to express the effect on pull of varying the normal load, the coefficient of traction is meaningless. When, however, small changes occur m the normal load (such as caused by weight transferred withm a vehicle or added from mounting an implement on a tractor), the coefficient is necessary in spite of its dependence on normal load. 7.4.3 Evaluation of Performance Evaluation of traction devices involves comparing the performance curves of different devices with subjective levels of performance that are required or desired. Devices may also be evaluated m respect to each other without specification of any level or standard of performance. Unfortunately, this type of comparison provides no common denominator for other evaluations. The difficulty m comparing complete performance curves such as shown in figure 262 is that they usually have different shapes for different traction conditions, and the curves for two similar devices will often cross m the same traction condition. Thus, for example, tire A may pull more than tire B at 10-percent slip, but the reverse might be true at 50-percent slip. The difficulty of comparing th^ curves can be greatly reduced if a single value can be obtained to represent the overall nature ot a particular curve H61). . ^^ ^^ ^ u One value which might be used is the maximum pull that can be developed. When a heavy load needs to be started or when a short distance is to be traversed in difficult trafficable conditions, maximum pull is perhaps the most important consideration. Maximum pull is 380 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE relatively easy to determine; unfortunately, it is often the only basis on which traction performance is evaluated. Where no clear maximum is attained as the percentage of slip is increased, some arbitrary slip range may be selected as a base within which a maximum IS determined. The range 0 to 70 percent has been used with some justification. At slips above 70 percent, excessive dig-in occurs and forward travel is reduced to the point where the device is nearly immobile. The maximum pull in the range from 0- to 70-percent slip might be used as a single value that reflects one aspect of the traction performance of a device. Another single value to reflect traction performance would be some average pull. In practice, maximum pull is seldom either required or attained. When operating in a given traction condition, a specific pull is required and the slip of the traction device adjusts until the required pull is developed. Sufficient input power must be available and the device must have the capacity to develop the required pull. The slip will adjust to the appropriate levels tor different magnitudes of pull. M:ost operators try to keep slip below some arbitrais limit, particularly when operating for long periods of time. If excessive slippage occurs, the operators will effect some change in operation to keep the slip under their arbitrary ^nf î^^^* ^^^^ normal range of slip thus exists where a device will be operated most of the time. In pneumatic tires, most sharp changes m slip-puU curves occur before 30-percent slip is attained. Most operators would probably consider 30-percent slip excessive and take steps to reduce it. Based on this assumption, the average pull for the range 0- to 30-percent slip thus provides a single member reflecting the traction performance over the actual operating range of the'tire. When performance is considered in terms of energy efficiency, power efficiency-pull curves can be meaningful in evaluating performance (29). Since efficiency becomes most important when the device is operating for long periods, usually at different states of slip and pull, an average power efficiency would probably be more useful than a maximum. The average power efficiency for pulls developed m the normal range of operation (0- to 30-percent slip) would provide a single value that reflects the energy efficiency aspects of traction performance in a range of probable operation. When energy efficiency is important, an additional factor must be considered. A work output-slip curve (equation 166) indicates the operative state at which maximum work can be obtained. If the pull associated with maximum work is the same as the pull associated with maximum efficiency, that pull would be the most suitable operating state. Generally, however, power efficiency maxi- mizes at a lower pull than does work output. The possibility thus exists that m some conditions a device may have high efficiency yet do little work, whereas in other conditions it may do considerable work but have poor efficiency. This possibility arises because a device can use a given amount of input power to develop a low work output at low slip so that the work is developed with high mechanical efficiency. The device could also utilize the same amount of energy to develop a higher work output at a high slip and, conse- SOIL DYNAMICS IN TILLAGE AND TRACTION 381 quently, operate at lower efficiency. Slip can thus be balanced against pull with varying effects on work output and power efficiency. . The product of work output (equation 166) and power efficiency is a dimensionless number that gives equal weight to both factors. The number may be properly defined as traction efficiency. A traction device may be visualized as a machine that requires weight and input power to make it operate. The purpose of the machine is to do useful work by developing pull at some forward speed. The number—traction efficiency—considers the influence of three factors : weight, output power, and input power. A maximum value of traction efficiency can be considered the optimum operating state of the device for a particular traction condition. A traction efficiency- pull curve would, therefore, give the traction efficiency of the device at various pulls. The average value for traction efficiency, computed for the range of pulls that would be anticipated in actual use, would be a single value that reflects overall traction performance. Traction devices can be readily compared with single value indices. When the performance of a series of devices is measured in a given traction condition, one device can be used as a standard and each device can be compared with the standard. By dividing the appropriate single value of each device by the respective single value of the standard, performance can be rated as a percentage of the standard. Each device can then be readily compared for a specific set of soil conditions. This can be extended to different soils. The percentage of performance of the standard for each device in various representative conditions can be determined, and these percentages can be averaged to give an overall comparison of the devices. If some knowledge of the anticipated time of operation on each soil condition can be determined, a weighted single value average could be determined that would represent performance m the anticipated soil conditions. These techniques provide a powerful means for evaluating traction performance. Cost of manufacture, adaptability to a particular vehicle, wear characteristics, and many other factors are needed before a particular device can be selected. Suitable traction performance, however, is one of the factors; and the criteria and measures of performance, together with the techniques outlined here, are the means for evaluating the factor of traction performance. 7.5 Design of Traction and Transport Devices Design implies intent or purpose; hence, designing a traction device implies that the device is to be constructed to accomplish some specific task or tasks. The success of the design depends on the degree to which the constructed device utilizes the ground conditions to best attain the desired performance. Several subtle but salient aspects are involved in traction design. Lack of a mechanics to integrate the various aspects into reliable mathematical expressions has caused considerable confusion. The confusion has probably^ resulted because individual researchers were primarily concerned with only one or two aspects of traction. The aims of the researchers often appear, to other researchers and to per- 382 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE sons trying to interpret the research results, to be different and dis- organized. A superficial review of technical literature confirms this observation. In a broad and realistic sense, however, the differences are only superficial and all efforts have had one common goal— the design of a traction device. The aspects of design will be discussed to show that the apparent confusion results from two approaches for obtaining design inforraation. Accurate mathematical expressions that describe the traction action and contain the factors affecting traction provide the best framework within which to design traction devices. Abstract traction design factors can be identified and their functional relations to each other and to performance can be determined. These factors are difficult to assess numerically and are similar in concept to those included in the tillage equations (equations 132 and 133). The factors are identified and their relations indicated in the force- traction equation, P = f{S,D,W,J), (168) where P — pull, S = soil, D = device, W = weight, / = relative movement, / = functional relation. Relative movement / is usually expressed as actual displacement for a nonrolling device and expressed as slip for a rolling device. Available knowledge verifies the general nature of equation 168; when a wheel carrying a fixed weight is operated on a uniform soil condition, a unique pull results for each slip. The variables are known to be independent because each can be varied over a reasonable range without being restricted by the remaining variables. Variations in S, D, W ov J will probably affect pull ; but a unique pull will result for each value of S, D, TT, or /. Within limits, a designer has control over factors B and TF. Thus, if a specific form of equation 168 were available, the device and weight factors could be optimized so that maximum pull could be obtained for various slips. Ecjuation 168 thus represents a traction equation that is useful for design. Only one equation is used to represent the action of a soil-traction device system whereas two equations are used to represent the action of a soil-tillage tool system. The force-tillage equation represents the input required to cause the action. The soil condition-tillage equation represents the output of the action that is of interest. In traction, equation 168 represents the output of the action that is of interest. A second force-traction equation that represents the input to cause the action is r = g{S,D,W,J), (169) where y represents the torque required to operate a rolling device. Equations 168 and 169 identify and represent the principal factors of interest in traction design. The relations between P and T are SOIL DYNAMICS IN TILLAGE AND TRACTION 383 analogous to the relations between F and Sf for tillage equations. P and T are dependent variables of the same independent variables and, hence, they may not be uniquely related. Available knowledge indicates that P and T are probably not uniquely related to each other. The action of a soil-traction device system is not intrinsically simpler than the action of a soil-tillage tool system. Changes m soil conditions are not normally of interest in the action of a soil- traction device system. Thus, they are not included in traction equations. A third traction equation Sf - k{Si, Z>, Tf, /) can be written when necessary, because the resulting soil conditions are precisely determined by S, D, W, and /. D in a traction equation IS roughly equivalent to Ts in the tillage equation and / and W are roughly equivalent to Tm. For a tillage tool, 7"^ inherently contains W since W influences the manner of movement (depth, for example) in a floating tillage tool such as a disk harrow. The independent variables in tillage and traction equations are very similar. The primary difference between the equations is our interest in the results of the action they describe. In tillage, the result of interest is the final soil condition and this is difficult to describe. In traction, the quantity of interest is usually the pull developed, and this can be measured directly. Soil-traction device systems have an additional simplifying aspect because the output described by the traction equation physically represents the limiting traction conditions. Seldom does available torque (the input that causes the action) limit pull. Usually pull is limited by other soil and machine factors represented in equation 168. Thus, efforts m traction research have been primarily concentrated on the factors represented in equation 168. _ Two methods are used to develop traction equations. Iîrst, traction equations can be derived from basic forms of behavior (sec. 7.2). Active behavior equations of soil quantitatively describe the soil action. Geometric equations and, in flexible devices, flexibility equations quantitatively describe the devices. Equation 160 expresses relative movement as a percentage of slip ; weight and pull are expressed as forces. The system of equations forms a mechanics, and the mechanics can be solved to describe traction. ^ _ A second method for developing traction equations is empirical and based on measured observations. The utility of the empirical approach is apparent when it is realized that many traction equations must exist. Every time different geometric equations, flexibility equations, or soil-behavior equations are used, a different traction equation probably will result. The parameters of the geometric, flexibility, and behavior equations assign numbers to^ the design factors. The parameters, in effect, become variables m a traction equation. A logical procedure is to relate pull to parameters of soil behavior and traction device description equations ( 36, 37 125 ). Equation 168 can be used as a guide to empirical approaches. The coefficient of traction is often calculated and graphically plotted in relation to slip to represent traction performance. Traction performance is, therefore, represented by a curve and the techniques 384 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE discussed in section 7.4.3. are used to evaluate performance. Equa- tion 168 then simplifies to a performance equation TP = h{S,D), (170) where TP — traction performance, S — soil, D — device, h = functional relation. The total differential of equation 170 can be written to indicate that changes in traction performance must come from a change in either the soil or the traction device. As a result, factors that inñuence traction performance can be compared to obtain design information. Comparisons have been widely used to obtain much useful traction design information. In comparative procedures, performance criteria are measured for one or more devices in a soil condition selected to represent expected operating conditions. Generally, no attempt is made to describe the soil condition in detail ; measurements are made to insure that the condition is identical for all devices. The performance of the devices is comparable only for that one condition. A direct comparison of the influence of factors on performance is valid since any change can be due only to differences in the devices. The superiority of one device indicates that the traction potential of the soil was more effectively utilized by that device than by the others. If comparisons in other representative soil conditions also show the device to be superior, it must have a better design than the others. Device descriptions can be used in manufacturing the new design. Comparative procedures can be used to identify suitable numerical representations of the design factor Z>. The geometry and flexibility of a device can usually be described in more than one way; therefore, numerical representation of the device is not always easy. Devices that are similar except in one identifiable difference can be directly compared; differences in performance can be attributed to the identified difference (for example, diameter). Comparisons can also provide data that indicate the importance of differences being studied. For instance, wheel diameter may affect traction niore than wheel width. If several diameters are compared, the diameter that gives the maximum pull (performance) can be considered an optimum. If the performance monotonically increases or decreases, a trend is established. Trends verified for several soil conditions provide the designer a choice of diameter sizes that he can use to meet the desired level of performance. Trends can be established for any design factor. Comparative procedures have limited use. They can never be used to predict the magnitude of performance. Also they lack the means for identifying soil behavior parameters. Since only minimum efforts are made to characterize soil in comparative procedures, attempts to develop even rudimentary correlations between soil and performance are impractical. Therefore, no reliable means is available to predict performance in a different soil condition. Lack of SOIL DYNAMICS IN TILLAGE AND TRACTION 385 a prediction capability does not negate the possibility of indicating trends. If a definite trend is established by comparative data, qualitative but not quantitative performance can be predicted. Thus, a trend might indicate that tire A will always pull more than tire B even though in some traction conditions both tires will pull less than in others. The inability to quantitatively predict performance and the incapability of identifying soil dynamic parameters severely limit the use of comparative procedures. A complete traction mechanics or a simplified empirical traction equation must include the effects on performance of both the soil and the device. In design, it is helpful to be able to derive a simpler specific design traction equation from the more complex soil-traction device mechanics. The derived design eqûation cannot be accurate unless the mechanics from which it is derived includes all pertinent soil and machine behaviors, unfortunately, we do not yet have this mechanics. Thus, the basic approach of developing a complete traction mechanics provides little assistance to contemporary designers. The limited application of comparative research data raises a question concerning its value. Research in soil dynamics is conducted to solve problems in mobility, trafficability, vehicle design, and traction performance. Results that apply in one problem-solving area may appear to have no application in others. When viewed m the broad spectrum of all problems, however, each specific solution may contribute to the solution of more general problems because of the insight that is provided concerning the behavior involved. Little emphasis has been placed on identifying dynamic soil parameters in comparative procedures so that one might conclude that the data serve no useful purpose. The direct comparison of designs has provided useful design information. Indeed, the design information available today is largely a product of this approach. Direct comparison of traction devices has been instrumental m identifying new design factors for the pool of traction knowledge. The development of radial-ply construction of pneumatic tires illustrates this fact. A comparison of tires demonstrated that radial-ply construction produced a traction advantage over conventional-ply construction. No traction equation could predict the improvement. Once the radial-ply factor had been identified, corrections could be made in both derived and empirical traction equations. Usefulness of comparative procedures does not condone their continuation. By following the concepts presented in tillage design equations (sec. 5.2), comparative procedures can be modified to provide data that contribute to the development of empirical traction equations. Restricted comparative procedures should be used only when the need for immediate information justifies their use. A research program using both derived and empirical approaches should provide a fundamental understanding of traction problems and also provide practical information. The apparent confusion one might read into traction research is not real. The ultiimte ffoal of traction is to be able to design and use traction devices, ihe goal is the same even though the methods followed to obtain the goal differ. 386 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE 7.5.1 Transport Devices Transport devices are simple insofar as their purpose is to support a load in such a manner that it can be easily moved over the soil. Their performance is determined by measuring the force required to pull a load over soil conditions that are of interest (sec. 7.4.2.). Because of its simplicity and adaptability, the wheel is the most commonly used transport device. In extreme conditions such as loose snow or sand, skids or tracks are sometimes used. Coefficients of shdmg resistance of 0.8 to 0.9 can be expected for steel on firm soil, but coefficients as low as 0.16 can be found in soft ñuid conditions ( .^74). Eunners can be used on snow since the coefficient of sliding resistance rarely goes above 0.3 for steel on ice or snow (S5), Because of the restricted uses of runners, however, most design information pertains to wheels. This discussion is limited to wheels and tracks. The composite design factors of a rigid wheel include diameter, width, and, to a limited degree, cross-sectional shape. For a pneumatic tire, some measure of ñexibility is also a design factor. Since the purpose of a transport device is usually to move a load, weight on the device is of paramount interest. The towing force required to move a load is a single value that may be measured to indicate transport performance. The coefficient of rolling resistance, is often used to characterize transport performance.

Coefficient of rolling resistance = ^, (171) TF' where F = towing force, W = weight carried. The relation has the same form as equation 153. Figure 263 shows the relation between towing force F and weight W for a pneumatic tire and a steel wheel of similar size for operations on a plowed loam soil (270). ^ The data show two important facts. First, since a straight line relation did not result for either wheel, the coefficient of rolling resistance was not a constant but varied with the load. Over small variations in load, however, a straight line would be a reasonable approximation of the relation. Second, the pneumatic tire could be towed much more easily than the steel wheel. Table 43 shows data reported by McKibben and Thompson ( 279 ) which indicate that the force required to tow a pneumatic-tired manure spreader was an average of 44 percent below that required for a comparable spreader with steel wheels. The machines carried a gross weight of 4,000 pounds and both wheels were as nearly the same size as possible. In every traction condition studied, the pneumatic tires required a smaller towing force than the steel wheels. In addition, the pneumatic tires had other advantages. For example, shock loads were reduced ( 108 ) and the tires showed less wear (96), The effect of wheel diameter, width, and load on transport performance has been analyzed by Freitag at the Waterways Experi- ment Station ( 134,^ 496 ). His analysis was based on information published over a period of approximately 20 years. Because of the SOIL DYNAMICS IN TILLAGE AND TRACTION 387

~~800 r~~

~~2000~~

~~LOAD (Lbs)~~

FIGURE 263.—Towing force required to roll various loads over a plowed loani soil : A, On a 6-28 steel wheel ; 7?, on a 6-16 pneumatic tire ; C, effectiveness of the pneumatic tire in reducing the towing force. (McKibben and Davidson, Agr. Engin. {210).) lack of characterization of soil conditions, only measurements on rigid wheels operated on loose sand were considered. Wheel loads ranged from % pound to 2,000 pounds; corresponding ranges in wheel sizes were used. Using ratios so that dimensionless numbers were available, Frei-

~~TABLE 43.—Reduction in towing force of a vehicle due to substituting pneu?natio tires for steel tires~~

Decrease in Soil condition towing force Percent P,nnf»rptp road - 5 Fall plowed, thawed soil 20 TîliiPfirrass sod - 30 TpTTinorflrv road on field 40 Burned sweet clover stubble 45 Wintpr rvp rousrh and frozen- 50 Sweet clover stubble and snow 60 ixravel road ^ 60 Cinder road 65 Fall-plowed, muddy soil, frozen underneath 67 Mean 44 SOURCE : McKibben and Thompson ( 219. ) 388 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE tag demonstrated that the towing force was proportional to TF^/^ (coefficient of rolling resistance increased with load). He also demonstrated that the towing force was inversely proportional to the diameter and that it could be related to the load per unit of width if a constant aspect ratio was maintained. For any wheel, the aspect ratio was defined as the diameter-to-width ratio. Figure 264

~~12 16 20 200 Y (lb/in)~~

~~FIGURE 264.—Rolling resistance-wheel parameter relations for rigid wheels on loose sand. ( Freitag, Auburn Univ. ( 134 ) • )~~

shows the empirical relations plotted for measurements made on rigid wheels of vastly different sizes operating on sand. These data originated from the findings of various researchers using dissimilar sands. The measurements were obtained under conditions ranging from laboratory-controlled indoor soil bins to fields where weather and other factors could affect the results. Nevertheless, definite relations are evident. They indicate that the rolling resistance—the towing force of towed rigid wheels operating on sand—can be related to other parameters in the form Fd 3/2

~~3600~~

~~3000~~

~~2400~~

~~1800-~~

~~1200~~

~~600~~

~~X 1000~~

~~FIGURE 265.—Rolling resistance-wheel parameter relations of various sizes of rigid wheels on sand and freshly tilled loam soils. (Replotted from data of McKibben and Davidson, Agr. Engin. {210),)~~

~~1200~~

~~1000-~~

~~800-~~

~~600~~

~~Ü. 400-~~

~~200~~

T^TPTTRF 266—Rolling resistance-wheel parameter relations of various sizes of rTgrn ilfon bluegrass sod and concrete. (Replotted from data of McKibben and Davidson, Agr. Engm. {210).) 390 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE in the other test conditions, some change may have occurred in the sod while the measurements were being made. The circled points may thus reflect a changed sod condition rather than scatter in the measurements. Figures 265 and 266 also show that the proportions between the factors m equation 172 may not be as simple as first indicated, bmce a best-fitting line does not pass through the origin, equation 172 has the form 17 \ 3/2 ^=.( T) +^' (173) where C = SL constant. Equation 171 suggests that two dynamic properties, which are common to the steel wheel and the medium, describe the behavior. Ke- gardless of the implications of K and G, the effects of composite design factors can be demonstrated by rearranging terms in equation 173 to give

where the terms are the same as those previously defined. Thus, increasing the diameter decreases the towing force and increasing the load on the wheel increases the towing force. But the effect of width IS not clear. Increasing the width decreases the left arm m the bracket of equation 172 but increases the right term. For values of i at infinity and zero, the quantity in the brackets becomes mñnite so that some minimum value must exist at intermediate values. Taking the partial derivative of the quantity in the bracket with respect to b and equating the derivative to zero provides a method for finding the minima and gives 1 5rTF3/2 2 53/2 ^ ^ - tF, and solving for b

~~^ = (^) W, (175)~~

which indicates the value of b that gives the lowest towing force. The effect of the shape of the wheel on the towing force cannot be determined from available information. The wheels considered by Freitag and by McKibben and Davidson had flat rims. One isolated comparison of different-shaped wheels indicated that both convex- and concave-shaped wheels required a slightly larger towing force, on the average, than a flat wheel of the same width and diameter. While the convex wheel required a larger towing force than the concave, the difference was small. The effect of shape appears to be much less significant than the effect of either diameter or width ( ^7^, 274 ). If a more exact evaluation of the effect of shape IS required, additional research is needed. Equation 174 can be shown to be generally applicable to pneumatic SOIL DYNAMICS IN TILLAGE AND TRACTION 391 tires. Freitag demonstrated that equation 172 applies if tires operating on loose sands are compared at constant deflection. Thus for a varying load, inflation pressure or size of tire must be changed in order to maintain a constant deflection. Deflection thus appears to be a measure of the flexibility of a pneumatic tire. Figure 267

FIGURE 267.—RoUing resistance-wheel parameter relations of various sizes of pneumatic wheels operating on: A, Concrete; B, bluegrass sod; C, silt loam soil. (Replotted from data of McKibben and Davidson, Agr. Engin. {272).) shows data replotted from McKibben and Davidson ( 272 ) where 16 pneumatic tires varying in diameter from 25 to 59 inches were compared in concrete, bluegrass sod, and silt loam soil. Deflection was not maintained constant during the loadings and measurements so that some scatter in the data can be attributed to this effect. In addition, nominal tire sizes were used so that the actual magnitudes of d and h are not accurate and these inaccuracies might contribute to the scatter. Although the applicability of equation 174 to pneumatic tires has not been clearly demonstrated, it appears to be a good first approximation of the relation. The appearance of two segregated groups of data for the bluegrass sod again suggests that instead of reflecting scatter in the data some change occurred in the operating conditions. The possibility of including a flexibility factor and a correction for the appropriate dimensions to improve the applicability of equation 174 to pneumatic tires constitutes a basis for additional research. Tracks have also been used as transport devices. The larger area of contact may be used to prevent sinkage and, as shown in figures 4 and 5, tracks may be used for support and control. The W^^^^*" ways Experiment Station ( 474 ) conducted an extensive series of experiments to measure the force required to tow tracked vehicles, wheeled vehicles, and sleds. The forces required to pull a tracked Athey wagon and a wheeled trailer are shown in table 44. The Athey wagon was fitted with two steel tracks 30 inches wide and approximately 60 inches long, whereas the wheeled trailer was fitted with 14-20 pneumatic tires inflated to 30 pounds per square inch. As a low-speed transport device, the tracked vehicle was superior to the 392 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE wheeled vehicle. The towing force required for the latter was at least 100 percent larger in nearly all instances. The performance results might be reversed if the two vehicles were operated on roads at higher speeds. Eecent developments in rubberized flexible tracks may overcome this limitation.

~~TABLE 44.—Towing force required to transport 12ß00 pounds over a sand-clay hlend on tracked and wheeled transport trailers~~

Soil condition Track-laying Wheeled (cone index) trailer trailer 1,000 pounds 1,000 pounds 20 __ _ _ 4.0 40- __ 1.8 60 1.3 80 _ 1.1 3.1 100 .9 2.4 150 .7 1.3 200 .5 .6 SouKCE : Waterways Experiment Station ( ^7^ ).

7.5.2 Driven Wheels The powered or driven wheel is the most versatile traction device available. Since the time pneumatic tires were adapted to the wheel to provide a degree of flexibility, the driven flexible wheel has become widely used. To illustrate, in January 1957 there were only 168,000 crawler tractors on farms in the United States but there were 4,432,000 wheeled tractors. Because a large number of driven wheels are used as traction devices, considerable effort has been made to obtain design information about wheels. Traction performance cannot be stated as simply for a traction device as it was for a transport device (sec. 7.4). Consequently, simple but rather complete relations such as those expressed in equation 174 have not yet been determined for driven wheels. In general, gross design factors describing the wheel have been individually related to some measure of performance to show trends in behavior. These gross parameters include width, diameter, and lug or grouser factors for rigid wheels. In pneumatic tires, measures of flexibility, carcass construction—that is, internal cord arrangement—rim width, and cross-sectional shape have been used. These parameters are not basic to traction behavior; rather, they are geometric and flexibility^ factors that the wheel designer must manipulate in order to obtain a practical design. Information relating gross parameters to traction performance is thus useful for general design purposes. Although the exact influence of individual basic pararneters on traction performance cannot be predicted nor can the optimum potential performance of a device be obtained by means other than trial and error, vastly improved traction systems have been developed by these techniques. The rigid wheel is a simpler traction device than the flexible wheel. Since the rigid wheel preceded the flexible wheel historically, it was the first to be studied as a traction device. Unfortunately, SOIL DYNAMICS IN TILLAGE AND TRACTION 393 most of the measures of traction performance that were discussed m section 7.3 have not been used in reporting traction data, usually, one or two measurable quantities have been determined and performance has been expressed in those terms. Davidson, Collms, and Mc- Kibben ( 95 ) primarily utilized power efRciency-puU relations to characterize traction performance. Figure 268 shows the effect of

~~500 1000 1500 2000 1000 2000 3000 4000~~

~~PULL (Lb)~~

FiGUBE 268.—Efifect of diameter (inches) on the traction performance of rigid wheels : A, On oat stubble tilled to a depth of 8 inches ¡B, on oat stubble. (Davidson, Collins, and McKibben, Iowa Agr. Expt. Sta. (äö ).)

diameter on the performance of steel wheels. As a general trend, increasing the diameter of the wheel increases the maximum pull the wheel can develop and also increases the efficiency with which any specific pull can be developed. The same effect was detected m both soil conditions studied. Possibly the trends can be generalized if additional data are obtained. A limited indication of the effect of lugs on traction performance is shown in figure 269 {95). Increasing the ength of the spade lugs increased the maximum pull that the wheel could attain, iiie data also showed that increases in lug height were accompanied by decreases in power efficiency below 20-percent slip. Presuniably, the extra effort required to force the longer lug m and out of the soil resulted in loss of energy and decreased efficiency. Although the data reported here only indicate possible trends, they do show that the factors investigated had a measurable effect on traction performance. The pneumatic tire has greatly extended the versatility of the driven wheel. The possible increase in field speeds due to their flexibility alone was perhaps sufficient justification for their acceptance m place of rigid wheels {m). Figure 270 shows that the Power efficiency of the pneumatic tire is much greater than that of the rigid 394 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~50 5 X 12 DIAGONAL 12 LUGS TOTAL 4 X 22 DIAGONAL g 40 Ö~~

~~5 30 4X9 4X6 SWkDE SPADE I 20 -> ^ 16 LUGS TOTAL~~

~~100 200 3ÖÖ 4ÖÖ 50Ö 600 TOO 800 900~~

~~PULL (Lbs)~~

~~FIGURE 269.--Effect of lug height on the traction performance of rigid wheels in a silt loam tilled to a depth of 8 inches. (Davidson, Collins, and Mc- Kibben, Iowa Agr. Expt. Sta. {95 ).) , ^ itxc~~

Steel wheel ( 95). When operating on packed cinders, the pneumatic tire could not develop a pull as high as the lugged steel wheel, but equivalent pulls were developed in other soil conditions. Measure- ments of wheel slip are not shown in figure 270, but they indicate that to develop a specific pull the pneumatic tire slipped much more than the rigid wheel. In spite of this slippage, more efficient traction was obtained, as measured by energy utilization. Initially the gain in power efficiency was attributed to a decrease m rolling resistance; this difference is shown in figure 268. Several

~~\ BLUEGRASS SOD UJ o~~

~~\i¡ \ PULVERATED SOIL~~

ÜJ

~~— ■ 12.75 X 28 PNEUMATIC TIRE 11.25X46 STEEL WHEEL~~

~~1000 2000 3000~~

~~PULL (FOR TWO WHEELS) (Lb)~~

FIGURE 270—Power efficiency of flexible and rigid wheels operating on several soil conditions. The pneumatic tire was fitted with chevron-type lugs % inch high; the steel wheel had 24 spade lugs 4X5 inches in size. Both wheels carried 1,125 pounds. (Davidson, Collins, and McKibben, Iowa Agr. üíXpt. bta. { 95 ).) SOIL DYNAMICS IN TILLAGE AND TRACTION 395 other factors may also be involved. For example, some data ( 95 ) indicate that a shorter lug height would contribute to the mcreased power efficiency. Since the coefficient of friction between rubber and soil is generally greater than that between steel and soil (figs. 104 and 105), much less lug or grouser action is necessary to shift from frictional failure to failure within the soil. Thus, the lower height of lugs on pneumatic tires may contribute greatly to the increased power efficiency. In reality, both the higher coefficient of friction and the lower lug height may indicate that the pneumatic tire does less work on the soil to develop a traction force than does the rigid wheel. The concept of optimizing the work done on the soil to obtain traction, as proposed by Steinbruegge (sec. 7.2.2), may explain part of the gain. Eesearch along these lines may reveal why the pneumatic tire is superior to the rigid wheel in terms of power efficiency. Whatever the reasons for the superiority of the pneumatic tire, there is little doubt that the designers of traction devices can attain greatly improved traction performance in most conditions by using a pneumatic tire rather than a rigid wheel. Of the various design factors for pneumatic tires, lugs have received the most attention. Perhaps one reason is that radical lug changes can be made without great changes in manufacturing costs. When diameter or width is changed, the amount of tire material may be increased or the method of construction may be changed so that manufacturing costs may be increased considerably. In addition, users have had rather inñexible requirements in terms of tire size. The opposite is true for lug design. Indeed, it is unfortunate that much traction research concerned with driven pneumatic tires has been conducted on commercially available tires. Too often a series of tires was selected for study m which more than one design factor was varied so that one factor could not be identified. The research results have often been a comparison or testing of two or more tires that indicated the superiority of one or more of the tires. The results do not provide information on the effect of any single design factor since in many cases the identity of the effective factor or factors could not be ascertained. Definitive information can be obtained only from a series of tires where the design factors are varied in an independent fashion. The cost of constructing a series of tires to meet the necessary requirements has probably deterred research. The most complete study of lug design factors was conducted by Reed and Shields {362), A specially constructed series of 37 experimental tires was used; sets of tires could be selected to independently vary lug height, lug spacing, lug angles, and other suspected composite design factors. The series used basically a 4-ply 11-38 tire carrying a constant static load of 2,185 pounds at 12 pounds per square inch inflation pressure. Measurements were made over a period of a year at the National Tillage Machinery Laboratory, and part of this information has been published ( SS^ ). The effect of lug height on traction performance for three soil types is shown in figure 271. The surface of the soil was not slippery nor was vegetation present on the surface of any of the soils. The data indicate, almost without reversal, that lower lug height 396 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~90- LUG HEIGHT(in) SAND -jr. LOAM CLAY SMOOTH ^^~~

~~il 13 15 II 14 17 PULL X 100 (Lb)~~

FIGURE 271.—Effect of lug height on the traction performance of pneumatic tires on sand, loam, and clay soils. (Reed and Shields, National Tillage Machinery Laboratory ( 362 ). ) gave better power efficiency. Except in sand, very little of the difference in maximum pull can be attributed to the change in lug height. Thus, the trend seems to be that the lower the height of lugs, the better the power efficiency with little effect on maximum pull. The tire with no lugs (the tire was constructed in a special smooth mold) in the loam soil shows what would probably have hap- pened if slipperiness had been present. The smooth tire was more efficient until it operated near its maximum pull. Its maximum pull was much lower than that of the lugged tires, which indicates that some grouser action was necessary to penetrate or dig through the surface to obtain more pull. Presumably the lug action enables the tire to change the traction condition. The change may involve a shift from frictional failure in the mutual contact area to failure within the soil, or the tire may secure more suitable traction by digging through the surface. The latter situation assumes a traction condition where some sinkage or dig-in places the tire in a different ground condition where more pull can be developed. The opposite condition can be envisioned, such as snow over ice or loose soil underlain by a dense wet soil layer. Once the upper layer is penetrated, the traction condition is poorer. Unless lugs or grousers are needed to penetrate through some special surface condition, shorter lugs appear to be better than longer ones. Lug height is obviously a composite design factor when considered from the standpoint of the tire. As lug height increases (with no other change in the tire), the lug becomes more flexible. The stiffness of the lug can be altered by rubber compounding or other means so that a force-deformation curve of the face of the lug relative to the carcass will be the same for all lug heights. In the data reported in figure 271, the tires were not adjusted to overcome the flexibility factor so that the influence of lug stability is included in the results. The importance of flexibility cannot be determined by an analysis of the data. Information from other sources does not indicate the effect of the flexibility factor. This factor must be isolated and SOIL DYNAMICS IN TILLAGE AND TRACTION 397 evaluated before conclusions concerning lug height can be made. Spacing of lugs is a second design factor that was considered in the extensive program of lug evaluation. The influence of lug spacing on traction performance is shown for three soil types in figure 272. The spacing of lugs was indicated by reporting the number of lug units on the fixed tire circumference. As the number of lugs

~~9 12 PULL X 100 (Lb)~~

~~FIGURE 272.—Effect of lug spacing (number of lug units) on traction performance of pneumatic tires on sand, loam, and clay soils. (Reed and Shields, National Tillage Machinery Laboratory (362).)~~

decreased, spacing between the lugs increased. The data indicate that power efficiency increased as lug spacing increased. Until a condition is encountered where grouser action is necessary to obtain increased pull, presumably the trend can be extrapolated to the condition where no lugs are present and the tire becomes a smooth tire. Technical difficulties during the conduct of the measurements were believed to have contributed to some of the erratic results m figure 272. The dotted extrapolation of the curve for the 26-lug tire and the apparently different behavior of the 23-lug tire m the clay soil cannot be fully explained. ^ . • i. ^ The data reported here do not indicate what effect lug spacing had on maximum pull. Since power efficiency approaches zero as slip increases, the respective curves shown in figure 272 do not give a reliable indication of the maximum pull that was developed. Fewer lugs, however, appear to contribute to increased power efficiency. It is possible that reducing the number of lugs increases power efficiency for the same reason postulated for reducing lug height. Since the soil is disturbed less with fewer lugs, less work has to be done on the soil to obtain traction. This line of reasoning suggests that when tires develop comparable pull, the tire that disturbs the soil least should be the most efficient. If such a conclusion is valid, the obvious interaction of lug height and spacing becomes apparent and indicates that they are composite design factors. 398 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE The effect of lug angle on traction performance is shown in figure 273. No general trend seems to be evident for the soil conditions studied. The effect of angle, however, seems to be less than that of lug height or lug spacing. The data indicate that maximum differ-

FiGURE 273.—Effect of lug angle on traction performance of pneumatic tires on sand, loam, and clay sous. (Reed and Shields, National TiUage Ma- chinery Laboratory ( 362 ). ) enees in power efficiency are on the order of 2 to 6 percent. The maximum differences obtained by altering lug height and spacing ran as high as 5 to 10 percent. No general trend in performance seems to be related to lug angle, but there is a measurable—though small—effect. Additional research may clarify the effect of lug angle on traction performance. Two other tire design factors were studied by Keed and Shields —tread width and radius of curvature of the tread. The length of lugs was changed so that tread width could be changed. As was true for the other lug factors, the tire carcass was not altered. No general trends in the relation between tread width and traction performance were evident. The effect was measurable and was slightly larger than the effect of lug angle but less than the effects of lug spacing and height. Changes in the radius of curvature of the tread essentially changed lug height from one end of the lug to the other. The lugs were of normal height at the center and gradually increased in height toward the shoulder. The result was a natter tread profile across the face of the tire. The results indicated a general superiority for the rounder profile (the tire with the shorter lugs at the shoulder). The effect was relatively small as compared to the effect of lug height. Additional work will be needed before the effect of tread width and radius of curvature of the tread can be fully evaluated. Vasey and Naylor ( 46S ) used six lug designs and a smooth tire (fig. 274) in a field study of the influence of lug design. While admittedly some lack of control of soil conditions exists in the field, sufficient care was exercised so that a direct comparison of the tires, except E and G on the plowed field can be made with reasonable SOIL DYNAMICS IN TILLAGE AND TRACTION 399

FIGURE 274.—Designs of tractor tire lugs studied by Vasey and Naylor. A smooth tire (G) is not shown. (Courtesy of the Tractor Testing Station, University of Melbourne.) confidence (^G^.). The performance of the tires on a bituminous road, a stubble-covered clay loam, and a plowed field is shown in figure 275. Power efficiency could not be determined from the measurements, but the data do reflect the pull capabilities of the lug designs. Several interesting comparisons can be made to show the effect of possible lug design factors. No generalized trend can be established, however, since the lug factors were not varied through a range. In the stubble-covered clay loam, the smooth tire could not develop as much pull as the lugged tires. Tire F was an industrial tire with a low lug and a closed center, which should be poor for penetrating the vegetation; yet the lugs gave greatly increased pull

~~3iOr~~

FIGURE 275.—Effect of lug design on traction performance of pneumatic tires: A, On a bituminous road ; H, on a stubble-covered clay loam ; 0, on a plowed fleld. (Vasey and Naylor, Jour. Agr. Kngin. Res. (^6^).) 400 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE as compared to the smooth tire. On the other hand, on the plowed field more aggressive lugs were apparently needed to obtain a large pull. Tires A and B, which had irregular and regular lugs, respectively, can be compared. The regular lugs appeared to be superior in each condition studied. Tires A and C provide a comparison of a straight lug with a slightly curved lug, the latter appearing to be better. Tire D had the most aggressive lug, and its performance was superior on the plowed field. Data in figure 275, A and a statistical study ( 4^4^ ) indicate that significant differences iir pull can be obtained by varying the lug designs on tires. Composite carcass design factors were studied following the introduction of the radial-ply tire. The concept of radial-ply construction originated in Europe and has been of interest because of the increased performance of that type of tire ( 124, ^V^-^ S78 ). Figure 276 shows sectional views of both conventional- and radial-ply construction. In the conventional tire, the cords run from one bead to the other at an angle of approximately 45°. In the radial-ply tire, however, the cords run from bead to bead at an angle of approximately 90° with the direction of travel. Other cords in the tread base area run circumferentially so that they intersect the direction of travel at an angle of approximately 5°; these cords have been termed a belt. Their function is to strengthen the radial plies circumferentially so they can transmit torque, which is applied to the tread base. Vanden Berg and Reed ( 461 ) studied the influence of carcass parameters on traction performance. A series of 10 experimental tires were used in which conventional ply, radial ply, narrow rim, flat tread base, and various combinations of radial-ply and narrow- rim construction could be studied (table 45). A smooth tire counterpart was also studied for each of the 10 experimental tires so that the effects of lugs and carcass could be separated. Pairs of tires that differ in only one design factor can be compared. Performance was measured with the tires operating on sand, sandy loam, silt loam, clay, and concrete. In evaluating the tires, the maximum coefficient of traction in the range of 0- to 70-percent slip, average coefficient of traction in the range of 0- to 30-percent slip and the average power efficiency for coefficients of traction in the range of 0 to 30 percent were used as measures of performance. The lugged tire with conventional carcass was chosen as the standard, and the performance for each tire was compared to the standard for each soil condition. By expressing the comparison on a percentage basis, the average percentage of improvement was determined for all conditions (table 46). The improvement attributable to individual design factors was determined by comparing the two tires that differed by the factor in question. Since the tires were to be used primarily for agricultural purposes, this type of analysis was also made considering only the sandy loam, silt loam, and clay soils. These results (table 47) show that, except for the smooth tires, the percentage of improvement for each factor was nearly the same as when sand and concrete were included. The close agreement between the two tables indicates the validity of using a limited number of traction conditions to represent the infinite number that actually exist. The data in tables 46 and SOIL DYNAMICS IN TILLAGE AND TRACTION 401

FIGURE 276.—Construction details: A, Conventional-ply tire designed for 10- inch rim with rounded tread base; B, radial-ply tire designed for 3Î4-inch rim with flattened tread base. (Wann and Reed, Amer. Soc. Agr. Engin. Trans. (^,70 ).)

47 permit evaluating the composite carcass design factors of radial- ply construction, narrow rim, and flattened tread base as well as the removal of lugs. 402 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~TABLE 45.—Description of experimental tires~~

Tread base Tire Tire Cord Rim No. treadi arrangement and carcass2 widths Inches 1 Smooth Conventional Rounded— 10.0 2 do Radial ply do 10.0 3 do do Flattened- 10.0 4 Lugged Conventional-__JElounded__ 10.0 5 do Radial ply do 10.0 6 do do Flattened- 10.0 7 Smooth do Rounded— 3.5 8 Lugged do do 3.5 9 Smooth do Flattened- 3.5 10 Lugged do do 3.5 1 The lugs and rubber were originally the same for all tires. Smooth tires were obtained by grinding the lugs off. 2 Tjjg ^^gg ^f ^jj^ tveo^á and carcass were circular for both rounded and flattened tires, but the flattened tires had a larger radius. 3 Tires were designed for the rim width indicated ; they were not stretched or compressed to fit the two rim widths shown. Figure 276, B shows a narrow rim.

~~TABLE ^^,—Effect of design factors on average improvement in traction performance of lugged and smooth tires in four soils and on concrete~~

Maximum Average coefficient of coefficient of Average power Design efficiency^ factor tractioni traction^ Lugged Smooth Lugged Smooth Lugged Smooth Percent Percent Percent Percent Percent Percent Smooth (lugs removed) -3 26.0 24.0 Radial ply construction-. 0 1 15 10.0 4.0 2.0 Narrow rim 2 2 6 4.5 4.5 -0.5 Flattened tread base -1 0.5 1.5 0.5 Total improvement of combined factors. -1 26 41.0 10.0 26.0 1 Determined in the range of 0- to 70-percent slip. 2 Determined in the range of 0- to 30-percent slip. 3 For coefficients of traction in the range of 0- to 30-percent slip SOURCE : Vanden Berg and Reed ( 46i ).

Several interesting conclusions can be drawn from the data, blippermess was not present in any of the traction conditions, but its elfect IS demonstrated in table 47 by the maximum coefficient of traction for smooth tires (lugs removed). The decrease in improvement reflects the necessity for grouser action to obtain maximum pull. On concrete and sand, grouser action is not necessary. The average coefficient of traction and average power efficiency clearly show that where maximum pull is not needed, a smooth tire is much more effi- SOIL DYNAMICS IN TILLAGE AND TRACTION 403

~~TABLE ^1,—Effect of design factors on average^ improvement in traction performance of lugged and smooth tires in clay^ silt, and sandy loam soils~~

Maximum Average Average Design coefficient of coefficient of power traction2 efficiency^ factor tractioni Lugged Smooth Lugged Smooth Lugged Smooth Percent Percent Percent Percent Percent Percent Smooth (lugs -25.0 14 21.0 Radial ply construction- -2 1.0 16.0 11 6.0 7.0 Narrow rim -1 0.5 4.5 6 5.5 -1.5 Flattened tread base— 2 -0.5 4.5 1 -0.5 -1.5 Total improvement of combined factors- -1 -24.0 25.0 32 11.0 25.0 1 Determined in the range of 0- to 70-percent slip. 2 Determined in the range of 0- to 30-percent slip. 3 For coefficients of traction in the range of 0- to 30-percent slip. SOURCE : Vanden Berg and Reed ( 46i ).

cient in energy transfer and will even pull more at lower slips. This confirms again the results of the lug-height study (fig. 271) and lug-spacing study (fig. 272) for pneumatic tires and the lug-height study (fig. 269) for rigid wheels. The fundamental prmciple of driven wheels is clearly demonstrated by the various studies of lugs. Except for maximum pull, no lugs are needed and their presence reduces power efficiency. The designer, thus, is faced with a compromise. Where poor traction conditions are anticipated for the major use, an aggressive lug may be required and justified at the expense of power efficiency. Where reasonably good traction conditions are anticipated, only a minimum amount of lug should be used so that power efficiency is kept high, yet a reasonable maximum pull can be attained. The information required by the future designer is the magnitude of grouser action needed to obtain a desired increase in maximum pull for the appropriate traction conditions. With such information he can effect the appropriate compromise. A second conclusion concerns the effect of radial-ply construction. The design factor had no significant effect on maximum pull in either lugged or smooth tires. However, a significant increase was obtained in average pull and power efficiency. Since the increase was reflected in both smooth and lugged tires, radial-ply construction must affect the manner in which forces are transmitted from the rim to the soil so that traction performance is increased. The factor, thus, is a carcass factor and suggests that considerable knowledge is needed in two areas: first, the distribution of stresses required by the soil for optimum traction; second, the manner in which carcass construction affects the transmission of forces from the rim to the soil-tire contact surface. The present state of knowledge indicates that radial-ply construction will not effect maximum 404 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE pull but will increase pull in the operating range of 0- to 30-percent slip and will also increase power efficiency in the same range. The carcass design factors of narrow rim and flattened tread base had varying effects on traction performance. Generally the effect of these factors was less than the effect of radial-ply construction. The difference in percentage of improvement between lugged and smooth tires also indicates an appreciable interaction between the carcass design factors and the lugs. Further work is needed to properly evaluate the two carcass design factors. Tables 46 and 47 indicate that traction performance improved slightly for each factor used with lugged tires. On smooth tires, the factors occasionally decreased performance. One final conclusion reflected in the data is the magnitude of possible traction improvement. The data in tables 46 and 47 suggest that the quickest gain in traction performance could be attained from a study of lugs. Presumably, lugs could be modified to retain much of the power efficiency gain of smooth tires along with some of the grouser action so maximum pull will not be too low for practical use. Minimum grouser action, radial-ply construction, narrow rim, and flattened tread base is the order in which possible improved traction might be attained. Several other composite factors have been studied by various researchers. The results of these studies indicate that the factors do affect traction performance in varying degrees. Inflation pressure is the only flexibility factor that has received more than rudimentary investigation. The general trend seems to be that as inflation pressure is lowered traction performance is increased. Inflation pressure is again not an independent factor. The increased performance may result from a larger soil-tire contact area as well as from an increase in flexibility. Certainly more research is needed before inflation pressure can be used as a design factor. Cleaning of traction devices, particularly lugged pneumatic tires, has received considerable attention although very few data have been published. Cleaning becomes a problem in sticky soil conditions where the potential maximum pull is low. Grouser action is usually necessary, and the adhering mud often fills up the spaces between the lugs and prevents grouser action. Shape of lugs, flexibility of lugs with respect to the carcass, and, recently, nonwetting agents such as polytetrafluoroethylene have been used to improve cleaning. No satisfactory method has been found to insure adequate cleaning in traction conditions where cleaning is needed. Dualing of tires is another factor that has been tried occasionally with conflicting results. Obviously, when two tires are far enough apart, they act as independent tires. Just as obviously, as they are brought closer together, at some spacing an interaction will occur. Practically no information is available on which to base any realistic conclusions concerning the effect of dualing wheels. Undoubtedly factors in addition to those discussed in this section are involved in the design of driven wheels. Such factors remain to be isolated and identified. Certainly, the effect on traction performance of many of the factors that were discussed requires more study if they are to be used intelligently in design. Until an accurate traction mechanics is available, presumably most useful design informa- SOIL DYNAMICS IN TILLAGE AND TRACTION 405 tion will continue to come from comparison procedures where composite factors and their interactions are investigated in a systematic manner by using the best scientific methods available. 7.5.3 Tracks The rolling track is a version of the wheel that has been used extensively in off-the-road applications. The large area of contact compensates for many minor irregularities in the terrain that make wheeled vehicles less desirable. The advantages of the track compared to the wheel need to be studied in the same way the advantages of the flexible wheel compared to the rigid wheel were studied. The composite design parameters that have been utilized to the greatest extent have been track width, track length, grouser shape, and grouser spacing. Only limited research has been conducted on tracks so that a sound basis for design is not always available. Nevertheless, in some situations the track has proved to be so superior to the wheel that measurements have not been needed to confirm the advantages. As with wheels, lugs and grousers have probably been given more attention than any other feature of tracks There are occasions when the penetration of lugs is necessary for the device to develop maximum pull. . 11 • Early work by Randolph ( SJß ) constitutes the only available information for individual lugs, but it is subject to interpretation since the measurements were made under conditions of 100-percent slip. One of the most significant findings of these studies was the establishment of a method of exploiting the so-called arch action of soil. Following the observations of stress distribution which had been studied earlier by Nichols and Randolph {320), designs were de-

~~(A) (B)~~

FIGURE 277.—Area of soU disturbed: A, By a single large lug; B, by several small lugs. 406 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE veloped to give smaller and fewer lugs. The principle, which it is suggested be henceforth called the Kandolph Principle, was later investigated by Dinglinger ( 103 ) and Kathje ( 3^2 ) in conjunction with studies of the action of simple tillage tools in soil (sec. 4.5.5). Figure 277 and table 48 show that the area of soil failed by lugs can be varied considerably by varying the size and spacing of the lugs. Bekker ( 36, 37 ) independently utilized the Eandolph Principle in spacing grousers along a tracked vehicle to prevent overlap of the areas of failure and to increase the pull of the vehicle. The spacing can be adjusted so that the grousers act independently of each other, as shown in figure 278, to give maximum traction for the minimum number of grousers. Figure 279 shows the effect of a spaced-link track design on the average pull of a tractor. The principle suggests that widening the track is another means of increasing traction performance. One complicating factor when widening the track is the conñict with

~~(A)~~

~~/^^^ W^//^ f//^^//^ ^7m~~

~~(B) wmimmmm ^WS^' "TTTW~~

~~(C)~~

~~FIGURE 278.—Effect of spacing of grousers on the area of soil disturbed: A, A single independent grouser ; B, multiple interacting grousers ; O, multiple independently acting grousers.~~

~~COEFFICIENT~~

~~eCXK) 10000 14000~~

~~TRACTOR WEIGHT (Lb)~~

FIGURE 279.—Effect of a spaced-link design on the traction performance of a tracked vehicle. (Land Locomotion Laboratory, Rpt. 31, 1958.) SOIL DYNAMICS IN TILLAGE AND TRACTION 407 other requirements of the makeup of the vehicle. The princij)le has also been applied to gun spades ( 2Jf2 ) where extending the width is not a limiting factor. In this case the spade can be collapsed during the transport stage but can be opened for use. These examples indicate that the Randolph Principle is one means of increasing traction performance of a tracked vehicle.

~~TABLE 48.—Influence of size and lateral spacing on the traction performance of lugged tires in sand~~

Dry loose sand Wet packed sand Lugs Lug Lug Pull per Pull per (number) 1 width spacing Total Total inch inch pull pull of lug of lug Inches Inches Pounds Pounds Pounds Pounds 5.0 53 10.6 67 13.4 2.5 41 16.4 51 20.4 .5 1.0 44 22.0 90 45.0 .5 1.5 35 35.0 47 47.0 1 Lugs were 1.5 inches long and were not buried when carrying a load of 90 pounds. SOURCE : Calculated from Randolph ( 3JtO ). Tracks are not loaded uniformly throughout their length, as was indicated by measurements shown in figure 247. The type of loading that should be applied along a track to obtain maximum traction is not known. That changes in loading inñuence the pull that develops was shown in early work by Davidson, Collins, and McKibben {95), The height of the hitch of a 7,700-pound tractor was varied to change the unit load applied to the soil by the tractor along the length of the track. As shown in figure 280, an increase in the load on the rear

~~I 2 3 4 5 6~~

~~PULL X 1000 (Lb»)~~

FIGURE 280.—Effect on the power efficiency of changing the load by elevating the hitch point on a tracked vehicle. (Davidson, Collins, and McKibben, Agr. Engin. {95).) 408 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE of the vehicle reduced the maximum efficiency and the pull at which it occurred. Eeed ( 35Jf ) studied the influence of varying the load by means of changing the width of the track. As shown in table 49 increasing the normal load on a clay soil increased pull. In sand, little influence was detected.

~~TABLE 49.—Drawbar full of tracks of different widths when loaded to Sß80 founds~~

Sou and Drawbar pull at— width of 10-percent 20-percent tracki 30-percent 40-percent slip slip slip slip Pounds Pounds Pounds Pounds Sand: 12 inches 2,010 2,150 2,150 2,010 16 inches 1,930 2,030 2,100 2,050 20 inches 1,900 2,100 2,150 2,120 Loam: 12 inches 1,700 2,100 2,400 2,500 16 inches 1,700 2,000 2,200 2,400 20 inches 1,700 2,300 2,400 2,300 Clay: 12 inches 3,100 3,500 3,520 3,520 16 inches 2,250 2,500 2,510 2,520 20 inches 2,250 2,350 2,400 2,500 1 Track length was 61 inches on a hard level surface. SOURCE : Reed ( 354 ) -

The magnitude of the vertical load on the grouser is important because it determines whether the lug is capable of penetrating the soil. If the lug can be fully seated in the soil, a greater pull can be developed. Eandolph ( 34Ú ), using steel wheels, demonstrated this principle and Payne ( 330 ) designed a winch sprag based on a theory that also utilized the principle. A lug or sprag, when fully seated in the soil (fig. 278, A)^ constitutes a mechanical system similar to that shown m figure 88, A for tillage tools. If one neglects the effect of the tip, the forces on the lug of unit width may be expressed as T = VsyZnan^ Í^ +-|-) + 2í7Uan (i-f). (176) where soil bulk density, depth of lug in soil, coefficient of soil-soil friction, cohesion. and the traction or anchorage that could be expected from the device can be computed. Based on logical assumptions, it was concluded that the maximum traction force that could be developed by such a device was due not only to a cohesive component of soil strength but also to a frictional component that could be increased by maintaining a higher normal load on the shearing surface. As a result, a new sprag that permitted this type of loading was designed (fig. 281). The sprag shown in figure 281 A utilizes a single inclined blade SOIL DYNAMICS IN TILLAGE AND TRACTION 409 to overcome a fixed soil resistance. The improved sprag shown m figure 281, B utilizes a horizontal plate to confine the soil in the failure area in such a manner that soil resistance may be increased by proper loading. As shown in figure 282, any increase in traction force T decreases tractor weight W on the soil with the weight being transferred to the sprag along line R, R should act coincidently with or below Ri in order to secure a deep ground failure. If the soil does not fail, the entire tractor may be lifted from the soil and its weight will be transferred to the sprag. Table 50 shows that considerable increase in traction was secured by the new design. As speed requirements have been increased, designs have been developed to introduce flexibility into track systems. Track sus-

~~^OLD SPRAG NEW SPRAG (A) (B)~~

~~FIGURE 281.—A, Conventional sprag with inclined blade; B, improved winch sprag designed with horizontal plate to increase traction by loading the soil. (Payne, Jour. Agr. Engin. Res. ( SSO ).)~~

FIGURE 282.—The forces on an improved winch sprag designed to load the soil faUure surface: W = weight of tractor, A-B = area of slip, s = shearing stress Ô = angle of soil-metal friction, T = maximum traction force, a - angle of failure (7r/4-0/2), R = resultant on sprag,

~~TABLE 60.—Influence of increasing the normal load on the failure surface of a traction device on traction performance~~

Son Improved Conventional condition sprag sprag Pounds Pounds Wet and plastic 7,000 8,000 Sandy loam 14,600 8,000 Sandy loam (grassy) 15,500 8,000 Clay loam cultivated- 14,500 11,000 Sandy loam freshly cultivated 15,750 8,000

SOURCE : Payne (. 410 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE pensions may be nonrigid, which permits a degree of vertical flexibility ; but each track shoe remains inflexible. Forrest ( 123 ), speak- ing for the American Eubber Industry, has indicated that rubber tracks offer great promise for agriculture since they provide low ground pressure intensities, are lightweight, and may be operated at much higher speeds than vehicles with metal tracks. A rigid high- speed metal track has also been developed. Bonmartini ( ^9 ) has designed a number of pneumatic flexible tracks for aircraft and other vehicles. Although the specifications and techniques of construction of flexible tracks are beyond the scope of consideration here, these are the factors that have slowed the development and use of flexible tracks. One of the more radical designs is a roller track. The individual track shoes are H-shaped and contain a roller in each of the open sides. During operation, the center bar of the H is perpendicular to the direction of travel and provides traction as do the rollers whose axes of rotation are mounted parallel to the direction of travel so that they do not roll. On turning, however, the lateral movement of the track is facilitated by the free-rolling movement of the rollers on each of the open arms of each H-shaped track shoe. The roller track can turn with only 50 percent of the torque required for rubber tracks and about 30 percent of that required for a steel track. Lateral movement on slopes is reportedly not a limiting factor of the design, and the maximum pull that can be developed on level land equals or exceeds the pull that can be developed by steel and rubber tracks. Slope stability has been increased by introducing an angle of 10° between each of the rollers and the center line of the track. Tracks will continue to be designed through the use of composite parameters. These parameters appear to be identical for tracks and wheels, when allowing for variations such as the relation of the radius to axle height. Other aspects such as vibration and soil compaction have been studied, and additional design information concerning these points is included in chapter 8.

7.5.4 Auxiliary Devices Conventional vehicles are designed to operate on average or normal soil conditions. When ground conditions are so extreme that conventional designs do not provide adequate traction or transport, new principles of design may be necessary. As an example, one might utilize the ground effects principle. An alternate to this action would be to convert a conventional design into a new^ design by equipping it with auxiliary devices that change the traction or transport capabilities. These devices wil be termed traction aids when they come into direct contact with the soil. Other methods of altering the design are discussed in section 7.5.5. The form and action of traction aids must be based on a method for overcoming some envisioned limiting traction condition. A typical case is a slippery surface underlain by a firm base. If a grip can be established between the traction device and the firm base, traction can be obtained. Indeed, under special conditions, the device is essentially geared to the soil so that a coefficient of traction SOIL DYNAMICS IN TILLAGE AND TRACTION 411

'« 4J 4-J 03 Ö ^ rS 1 Ol Pi ^•o coa t- r«^ 4J -M 1 8 8^^ vA TH (N C^ GO 3^^ ä «> ^^ (1^ ft

r< ^ 00 5^ -M -»-3 ci Ö ^ O CD O 8 O t' ce Co" 3^ S'^ TH r-î T-î ci .2 a p^ ft Î ^1 §^l ce S-" gÍ3 8 î:5g8 O Cj O S a» TA r-î r-î C^* 1 CÖ ^ .. •§ -4J +J 8 8g8 pi 't:^ 3^ ë^ r-î rHr-îc4 rf o «2 ^ PH ft « o 11 ^ 2 s 8 p looq ga^^ T-Î T-î r-î r-î

+-> 4J CO CD 00 8 O iO CO rH rH (N a« Ci^ ft '-tó %n s- cá 2 s 8 ë^S ;^ a » T-Î r-î r-î TA •^ -M +J 1 a; ft 8 05 ÍÍ5 00 3^ S * r-î * r-î T-î pLi ft «ï) 1 cj 2 í3 8 8g§8 gaa TH r-î r-î r-î •iS> <ï) 1 1 03 Cj 02 1 -S 1 i 1 i i o'^ a 2 5 ' 1 1 §12 *o3 O ft 1 1 1 P-H o3 bu d 02 œ 1 1 1 'd'ö d °f o Oí ?> 1 1 02 o a> 0) 1^ ^P -M +-» (D '-M 03 c3 Wi 4^2 S i 1« *-M *4-> 4J 13 .è ,^Qa2W r-l (N 00 H 1

FIGURE 283.—Wires used to cut mud from a rolling wheel to prevent immobilization of the vehicle. SOIL DYNAMICS IN TILLAGE AND TRACTION 413 less than the rubber tire to which they are attached, they will not touch the highway. Traction aids may be designed to improve the self-cleanmg qualities of devices. For example, figure 283 shows the use of short lengths of tightly stretched wires to cut mud from a rolling wheel. While cutters or scrapers may prevent an undesirable buildup of soil, they require an additional input of work to remove the soil. Use of polytetrafluoroethylene or other materials on devices may prevent soil buildup by reducing the adhesion of soil to the device. 7.5.5 Operational Control of Design Factors A number of design factors can be modified, adjusted, or controlled by the operator to improve the traction or transport performance of a vehicle. Although the exact nature of their influence may not be known, their immediate effect on performance can be observed and adjusted. In a final analysis, the operator should be able to adjust all parameters to meet individual operating conditions. The simplest example of this type of control is altering the inflation pressure of a pneumatic tire to provide different tire deflections and changes in rolling resistance {271), Decreasing the inflation pressure may improve traction performance in some operating conditions. As shown in figure 284, the pull of a tire may be increased by deflating

~~^'205 4ÔÔ 600 8ÖÖ IOC» 500 1000 1500 2000 2500 3000 DRAWBAR PULL (Lb»)~~

FIGURE 284.—Efeect of altering the inflation pressure of pneumatic tires on traction performance in sand, clay, and concrete. the tire when operating on sand, whereas there may be no effect on clay. The flexing of deflated tires requires additional energy ; therefore, the power efficiency of a tire operating on concrete may be decreased by deflation. The weight on a traction device may be altered to improve traction performance. Normally, weight is added to the vehicle to increase pull. How the weight is added should be of minor importance, but practical considerations might alter this. Reed, Reaves, and Shields ( 861 ) have reported a complete equivalence of mechanical weights added on an axle and weight .added as a liquid ballast inside the tire. The added pressure on the inside of the tire carcass did not seem to appreciably alter the stresses or their distribution m the mutual contact area. Powdered soil materials have also been used as ballast in tires, but the heat generated by friction during rolling might be objectionable. Fluid in tires had little influence on 414 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~4J -M 22 CO rH ^H lO o JPH 8 (M^ o ÍO y^ 3^ g'^ TH TH TA rA ci P-i a Ö2 , <.ñ Ci ^ ■SisOS i2 i3 8 ^ a i=^ T-î TH TA vA oi~~

~~8 rH ^ j TH TA piH a a '-> gÍ3 8 S 8 g ^ gaa TH r-Î rH rH C^* o .-s~~

~~8 CO 8 8 S a, TA rH rH (N 2a- .3 a~~

g" Ci . 4-Í 8 CO ?1 !§ S? O 5 O ^ a a T-H íH TA TA (N ,CJ Q .. 4^ 4.. ci fl ^ 8 8 CO rH a« TA rA (M* .2 a ill a ■gg 8-^ 00 gÍ3 8 CO S ^ S? ^aa TH r-í rH* rH rA ci 4-2 4-> 1 1 a> a l> Ci iO 8 1 a« 1 TA rH C^ .sa fil a •tí5 Sai S-^ Mgö 1 ÏO rH t- 3 s í3 S 1 TH -^ CO ce ^ a ft TA ' TA T-î Oi

~~4^ 4^ ÏO t- rH ;0 8 o Ci ^ CO T-î TA (>>iH rH* 00 00 cô 25 (N~~

~~o a I- -I o (O LÜ £ Ü. 5 o~~

~~(B)~~

~~FIGURE 285.—Fitting tires on a vehicle to promote cleaning. Tlie direction of relative motion between the tire and the soil: A, may pack soU between the lugs; or B, may scour the area clean.~~

shows two ways that lugs may be oriented to the direction of travel. In figure 285 J., wheel slip packs soil between the lugs and reduces their effectiveness. But in sand or gravel or other conditions where there is no adhesion, fitting tires as shown in figure 285, A may provide greater traction rather than less. Traction devices may also be cleaned by reducing the inflation pressure to the point where flexing is sufficient to assist in dislodging compacted soil. These few examples show how the operator can control design factors. The examples also indicate the need for a fundamental mechanics that will enable intelligent control of the various factors. 416 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Changing the height of hitch (fig. 280) for tracked vehicles is another example. In four-wheel-drive tractors, a change in load distribution occurs with a change in height of hitch. The operator will need simplified instructions or a simplified means of evaluating a situation in order to make an intelligent decision. Obviously, the operator cannot justify running through a series of lengthy calculations to obtain information on which to base a decision. All design factors that are subject to operational control must, therefore, be translated into simple relations in order to obtain the best traction possible. Very little information is available in such a form today. While no particular point has been made of operator skill, it is obvious that the actual manipulation of vehicles is of paramount practical importance in securmg traction and transport in difficult soil conditions.

7.6 Vehicle Design, Use, and Performance The mechanics of traction and transport includes all forces acting in the soil-vehicle system. The design of the individual components has been considered so far, bujb in practice these components do not always act independently. Thus, a vehicle may operate in such a way that the forces differ on each wheel. As a result, each wheel may require a different design or method of operation for the entire vehicle to operate at its maximum theoretical efficiency or effectiveness. 7.6.1 Vehicle Morphology The actual morphology or form of a vehicle can be designed to utilize the maximum traction performance of the individual support and propelling devices. For example, the front and rear wheels on the side of a vehicle may be in line so that they run in the same track, or they may be offset so that each makes its own track. When the wheels run in the same track, the rear tire operates on compacted soil, and the pull and power efficiency of the rear tire generally differ from those of the front tire even though both may be powered wheels ( 273^ 358 ). In addition, the amount of sinkage or soil compaction that occurs when the wheels run in the same track is less than when they operate in separate tracks. The total load resistance that traction devices must overcome includes all forms of motion resistance : rolling resistance of transport wheels, any drag resistance between the vehicle and the soil, wind resistance, resistance by brush or other vegetation, and drawbar pull requirements. Under conditions of operation where there is deep sinkage in the soil or where there is passage through dense vegetation, structural parts of the vehicle may drag and cause considerable motion resistance. The Waterways Experiment Station ( 125^ 220 ) has developed a mobility index to evaluate vehicle morphology in a form that can be used to indicate a vehicle's mobility performance. Examples of morphologic parameters included in the index for self-propelled wheeled vehicles are as follows: SOIL DYNAMICS IN TILLAGE AND TRACTION 417

~~^sontact weight pressure X factor factor Mobility = 0.6 + wheelload index tire X grouser . factor factor~~

trans- clearance X engine X mission + 20, (177) factor factor factor where gross wt. (lb.) contact pressure factor = tide width X rim diam. X No. of tires' weight factor: greater than 35,000 lb. = 1.1 15,000 to 35,000 lb. = 1.0 less than 15,000 lb. = 0.9, tire factor = 1.25 X tire width in inches divided by 1.00, grouser factor: with chains = 1.05 without chains = 1.00, wheel load = gross wt. in kips (wheels may be No. of wheels single or dual), clearance factor — clearance in inches, 10 engine factor: greater than 10 h.p./ton = 1.00 less than 10 h.p./ton = 1.05, transmission factor: hydraulic = 1.00 mechanical = 1.05. The mobility index is a specific characterization of a vehicle since it includes only vehicle parameters. Indices have been developed for self-propelled tracked and wheeled vehicles and for towed tracked and wheeled vehicles. Empirical correlations have been made between the mobility index and vehicle cone index measurements. Vehicle cone index measurements (sec. 3.3.1) were made on soil to determine the minimum strength required for 50 passes of the vehicles in the critical soil layer (6- to 12-inch depth zone). The mobility indices of new and uncharacterized conventional vehicles have been predicted with considerable accuracy by means of these relations so they are of practical significance. Based on empirical relations such as these, it is possible to analyze the morphologic factors that have a pronounced influence on vehicle performance. This analysis may be a means for detecting objectives for improved designs. 7.6.2 Vehicle Capabilities The capabilities of vehicles may be varied by different designs to meet certain forseeable requirements. A common example of this is 418 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the construction of all-wheel-drive vehicles. Powering of all wheels not only may eliminate the rolling resistance of any towed wheels but also may add to the traction force that can be developed by the vehicle ( 156, 358, 504), A consideration of power efficiency-slip relations on different soil conditions might indicate that the leading and following wheels on a vehicle should be operated at different slips to achieve maximum efficiency. A form of controlled wheel slip is achieved by wheel braking or by using differential locks. Data reported by Geiger ( HI ) and Seuser ( 38^ ) indicate that use of a differential lock prevented undesirable slip when plowing with one wheel in the plow furrow. Control of the slip eliminated the need for wheel weights. Individual motors on wheels provide another means of obtaining controlled wheel slip. Depending on need, all-wheel drive may be used to improve traction performance without adding weight or using other traction assistance such as winches or tow vehicles. These last two methods of securing propulsion recognize that the traction capacity is inadequate and they also consider that the requirement is very infrequent. Thus, use of a tractor to push a large earth-moving machine while cutting and loading may represent a more practical means of supplying power than to redesign a larger and more powerful unit that will be used to capacity only on an infrequent basis. Gross flexibility can be designed into vehicles in a similar fashion. Articulated vehicles permit a measure of steering and climbing capabilities that cannot be obtained by orthodox vehicle designs. The Meili Flex-Trac is a six-wheel vehicle with a vertical articulation capability. Since any pair of wheels can be elevated, the vehicle can be adjusted to conform to rough terrain so that the traction capacity of all wheels can be brought into use. Horizontal articulation facili- tates the steering of extremely long vehicles, especially when tracks are used. Kereselidze, Khukhuni, and Shkolnik ( 216 ) and Lange ( 250 ) have developed hillside tractors that can redistribute the load of the vehicle on slopes to increase traction and stability. Soehne ( 400 ) has used a rolling disk to stabilize vehicles on slopes. One novel capability that can be added to vehicles is lift. The inclusion of a fan to create a ground effects machine may reduce the axle weight or completely lift the vehicle in nontrafficable conditions. At the point where the complete weight of the vehicle is balanced, the vehicle is no longer a ground-operating vehicle. Special vehicle capabilities must be designed into the vehicle. That is to say, information must be made available to designers to provide a basis for the designs. The value of any particular design must be based on a realistic assessment of its importance and frequency of use. Some optimum balance between expense and need would have to be reached to determine when any particular design would be practical. These designs are then developed to exploit the traction capabilities of the individual traction and transport components of the vehicle. SOIL DYNAMICS IN TILLAGE AND TRACTION 419 7J Relative Importance of the Soil and the Vehicle on Traction and Transport Capabilities Traction and transport are obtained from forces transmitted through the mutual area of contact between the soil and the vehicle. The nature and magnitude of the forces depend on the characteristics of both the soil and the vehicle. Such an assumption was discussed in the introduction of section 7.4 and was expressed in mathematical terms in equation 168. Some of the composite design factors of the vehicle that influence traction performance were discussed in other sections of this chapter. The fact remains, however, that the soil has a greater influence on traction and transport capabilities than does the vehicle. On pavement, vehicles can develop high pulls; but when operating on soil, they may develop only a fraction of the pull they develop on pavement because of the adverse soil conditions ( 1^22 ). For this reason, off-the-road operations represent a widespread problem in design and use of vehicles. Figure 286 illustrates the importance of traction conditions on performance. The experimental tire had radial-ply construction, narrow rim, and no lugs, whereas the control tire was a typical agricultural tractor tire. The data indicate that, except on concrete, performance was affected much more by traction conditions than by

~~10 20 30 40 50 60 70 SLIP (%)~~

FIGURE 286.—Relative effect of traction conditions and traction d^ice design on the performance of two 11-28 pneumatic tires. (National TiUage Ma- chinery Laboratory.) 420 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE the rather radical design changes of the experimental tire. Even within one so-called soil type, traction conditions have a great influence on performance. Table M shows the force required to pull two types of trailers across a soil having various cone indexes. The cone index indicates a combined change of various physical properties in the soil that reflects a change in strength. The data indicate that soil has a large effect on towing force, certainly as large as the difference between the tracked trailer and the wheeled trailer. For any vehicle, therefore, the soil condition will determine the traction performance to a much greater extent than any operational control factor or design factor. Because of the large influence of soil conditions on traction performance, predicting performance becomes extremely important when a device is to be operated on a wide range of soil conditions. In those circumstances (for example, military operations) a means of predicting performance would provide a means for determining whether the vehicle will be useful—that is, capable of accomplishing its purpose. Even further, however, if alternate soil conditions or paths of travel are available, a suitable path can be selected so that in effect the vehicle is adapted to the land. Because of the importance of predicting magnitude of performance, many attempts have been made to relate performance to soil conditions. Two of the more successful attempts have been discussed. As was pointed out, the relations between traction and transport performance must describe the forces in the area of contact. Since this nature is extremely complex, empirical correlations have been substituted in lieu of a more fundamental approach. The nature of the behavior must be considered even in empirical correlations, or the application of the correlations will be extremely limited. Truly, Sir Isaac Newton must have seen many apples fall before he was able to conclude the reason for falling. Similarly, the reasons for traction and transport performance must be determined if behavior is to be adequately described. Four aspects of design were outlined in the introduction to section 7.4. Kesearch concentrating on these four aspects will give insight into the reasons for traction performance and eventually lead to a solution of the problem. 7.8 Predicting Traction Performance Mathematical models of soil-traction device systems—that is, traction equations—have not been developed to the point where performance can be predicted. The urgent need to be able to predict performance, particularly for military mobility, has led to the development of simplified traction equations that can predict performance with limited but acceptable accuracy. Most of these equations have been empirically developed. Because soil and its condition greatly influence traction, the assessment of soil conditions has been emphasized while characterization of the traction device has been deemphasized. These traction equations have usually applied to a soil-vehicle system rather than to a soil-traction device system. In other words, the vehicle is considered an entity rather than a group of traction or transport devices, or both. These prediction equations SOIL DYNAMICS IN TILLAGE AND TRACTION 421 are not particularly useful for design because they emphasize predicting performance, because they are not sufficiently accurate, or because they are restricted to special situations. Nevertheless, these equations are examples of empirically developed traction equations. Soil behavior was shown to be associated with soil physical properties in sections 3.1 and 6.1. The possibility thus exists of establishing a correlation between a classification of these properties and vehicle performance. For a number of years soils have been classified with respect to their formation and use for crop production ( 4,^6^ JfJf7^ Ji^Iß ). More recently soils have been classified for construction and trafficability purposes ( 10^ 63^ 1^50^ JßJi^ ^95 ). The U.S. Army Corps of Engineers ( ^9^ ) and the Bureau of Eeclama- tion ( 450^ 477 ) have unified these classifications to some extent. The classifications are based on physical properties that are determined by standardized methods and that indicate certain behavior characteristics. The association of the physical properties and behavior characteristics is the justification for trying to relate classification of soil properties to vehicle performance. Physical properties that have been measured and used as a key or index to classification include: graduation of particle size, consistency, porosity or void ratio, specific gravity, moisture content, bulk density, penetration resistance, unconfined compressive strength, and soluble salts ( 15, 99,18^, 258, ^50 ). With some experience and judgment one can interpret these indexes in terms of dynamic behavior and relate them to vehicle performance. Texture of soil is one method of classifying soil physical properties into possible types of behavior reactions. Soil mapping programs based on texture classification have been made for many soils, and this information is readily available. One of the most widely used is the USDA Soil Classification System (fig. 287, A), The Unified Soil Classification System is shown in figure 287, B, As figure 287 shows, knowledge of a particular soil in one system can be translated to the other system. Textural classifications are based on the particle sizes of the mineral constituents of a soil. Moisture content, organic matter, and structural condition are not reflected in a textural classification. Organic matter is usually a small fraction of the total soil volume and remains relatively constant with time. Wlien the organic matter is a small fraction, its presence is usually ignored. Highly organic soils are encountered, however, and their physical properties are often influenced more by organic content than by mineral content. Mucks and peats are examples of organic soils, and new classification systems are being developed for them ( 389, U9). Several attempts have been made to integrate soil classification and machine factors into a scheme that would predict performance. Often these schemes were not represented by an equation, but they were represented graphically so that a quantitative prediction was possible. The most widely known scheme utilized the Casagrande ( 63, Í21 ) soil classification to design airfields. The strength of soil, determined by the California Bearing Ratio test ( 369 ) or from soil classification data, was correlated with the thickness of pavements and base materials that were required to support aircraft of 422 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~100 i~~

~~100 100 ^SAND (7o) (A)~~

~~100 100 SAND (%) ^ (B)~~

FIGURE 287.—A, USDA Soil Classification System; B, Unified Soil Classifica- tion System. (Waterways Experiment Station ( W )•) various weights. These correlations provided a design chart for the construction of flexible airfield pavements. Knight and Meyer at the Waterways Experiment Station ( ^^ ) SOIL DYNAMICS IN TILLAGE AND TRACTION 423 used a soil classification system to estimate the probability of a vehicle being able to successfully cross a specific soil. The estimation is based on comprehensive empirical correlations ( Jf9Jf ) that establish the probability that different soil strengths will adequately support the passage of different vehicles. The vehicles were characterized by a vehicle cone index, which was the minimum rating cone index required by the vehicle in order to complete 50 passes over the soil. Soil was characterized by a rating cone index that was measured with a cone penetrometer. The rating cone index of any soil could be determined by direct measurement so that a means was available to predict "go" or "no-go" for any vehicle whose vehicle cone index was known. Knight and Meyer extended prediction possibilities by predicting the rating cone index of a soil from the Unified Soil Classification system (fig. 288). As show^n in figure 288, the probable rating cone

~~VEHICLE CONE INDEX SOIL 60 60 . TYPE PREOOM ^/lEDIAN SYM SOIL RCI SP CLEAN SAND - CH FAT CLAY 122~~

~~CL LEAN CLAY 85~~

~~SM SILT Y SAND 85~~

~~ML SILT 77~~

~~OL ORG. SILT 54~~

~~PT PEAT, MUCK 45~~

PROBABILITY OF VEHICLE "CO" ON LEVEL TERRAIN I I EXCELLENT-GREATER THAN 90 •/• Clî^ GOOD - 76 TO 90 «fe F7771 FAIR-50 TO 75*7» ■■ POOR-LESS THAN 50 •7*

FIGURE 288.—Scheme, based on a textural soil classification system, for predicting the probability of a vehicle being able to cross over soil. (Knight and Meyer, 1st Internatl. Conf. Soil-Vehicle Systems Proc. {Jt92).)

index of a soil can be estimated from knowledge of a soil's textural classification, as shown in figure 287. Knowing the vehicle cone index then permits determining the probable passage of a vehicle. For example, in a soil type designated ML (silt), vehicle C would have a 50-percent probability of passage while vehicle A would have a 90-percent probability. This scheme does not consider the condition of a soil ; consequently, its accuracy is limited. The condition of a soil can vary from a ñuid to a rigid mass, depending on its moisture content, soil type, and previous history. Since a textural classification cannot indicate much about a specific condition, some means for assessing a soil condition offers a better means of predicting traction. Penetrometers (sec. 3.2.2.1) have been used to assess soil conditions. McKibben and Hull ( 277 ) used the penetration resistance of a soil as a means of predicting the coefficient of rolling resistance (towing 424 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE force/load on wheel) of a 7.50-28 pneumatic tire. The coefficient was expressed in the form y = 0.06a? + 0.021, (178) where y — coefficient of rolling resistance, X = penetration resistance. Nothing in this simple relation permits one to predict the rolling resistance of any other wheel; however, the results indicate the validity of the approach. The most intensive program in which an attempt was made to use a penetrometer to assess soil conditions is that of the U.S. Army Corps of Engineers Waterways Experiment Station. A cone penetrometer was developed that utilizes a 30° right circular cone (472). The tip is % square inch in cross section and has a smaller shaft so that no frictional forces are built up after penetration of the tip. The soil resistance to penetration is measured by an optically indicating dynamometer (proving ring) as the instrument is pressed into the soil and the resistance is expressed in units of stress (p.s.i.). Based on this instrument, a system of evaluation has been devised to predict the trafficability of soil for 50 passages of a vehicle ( 126 ). The repeated passage of vehicles in one path kneads and compacts the soil, which can either increase or decrease its strength. The net effect is to provide a new soil condition for each succeeding vehicle and even to successive wheels on the same vehicle. Measurements, therefore, are required to reflect both the initial and final soil strength. These measurements are made in the following manner : a sample of the top 12 inches of soil is collected in an undisturbed condition in a tube, and the average penetrometer reading is determined ; this reading is called the "cone index." The soil is then subjected to a standard tamping procedure during which the soil is "remolded" by 100 blows of a hammer. The remolding simulates the disturbance that occurs with the passage of 50 vehicles. A second penetrometer reading is taken after the soil has been remolded, and this value is called the "remolding index." Based on these two soil values, a "rating cone index" is computed for the soil where Rating Cone Index = Cone Index X Remolding Index. A vehicle evaluation system was developed simultaneously with the soil^ evaluation system. Initially, the vehicle system involved experimentally determining a rating cone index for the soil condition that would allow just 50 passages of the vehicle. In such a manner, each vehicle could be assigned a "vehicle cone index." Any soil condition that produced a rating cone index equal to the vehicle cone index, or greater, would be trafficable for that particular vehicle. Figure 289 shows typical relations between the rating cone index of soil and the towing force of sleds and vehicles. Figure 290 shows typical relations between the rating cone index and the predicted maximum pull where rating cone index is expressed as points above the vehicle cone index. Vehicle cone index defines the situation where the vehicle is self-propelled and does not necessarily develop useful pull. The success of the Waterways Experiment Station approach is gratifying and probably is due partly to the simplicity of the penetro- SOIL DYNAMICS IN TILLAGE AND TRACTION 425

~~100~~

~~VERY STICKY SOILS~~

~~STICKY SOILS~~

~~WHEELED VEHICLES o o: O ^30,000 lbs.~~

~~P 40 80 120 160 200 RATING CONE INDEX~~

FIGURE 289.—Typical relations between the rating cone index and the towing force required for sleds and vehicles. (Foster, Knight, and Rula, Water- ways Experiment Station ( 125 ).) meter and partly to limiting soil conditions to loose sand and wet saturated clay. These conditions provide the poorest trafficable situations and so are logical restrictions. As figure 290 shows, more accurate predictions are obtained than by the scheme shown m figure 288. The added accuracy results because the condition of a soil is considered and more factors that affect traction are assessed and included in the prediction relation.

~~TRACKED VEHICLES WITH , 70|- GROUSERS LONGER THAN 1^-~~

~~WHEELED VEHICLES~~

~~+30 +40 +50 +60 +70 RATING CONE INDEX (POINTS ABOVE VEHICLE CONE INDEX)~~

FiaiiRE 290-Predicted maximum puU on level ground versus rating cone ^"^ll.l%v:áTL points above vehicle cone index. (Knight and Rula, at the Waterways Experiment Station ( Ji\)¿ ) • ) 426 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE An equation to represent a curve in figure 290 would be a traction equation of the type indicated by equation 168. There is a need to identify accurate parameters that represent the soil and the device abstract factors and to determine the functional relations between the parameters. Dimensional analysis is a technique that assists m determining the functional relations. The US Army Transportation Research Command ( Jt32, 433, ^35 ) has used this technique to develop a traction equation for vehicles in sand. Di- mensional analysis procedures provide a method for combining various parameters that are believed to represent a system into a group of dimensionless terms designated as Pi terms. The most complete version of a dimensionless term equation had the following form:

TF - ^ U' 0,d^^ ^'^'^' ^' -j-J.S,B,y (179) where D = drawbar pull, W = gross vehicle weight, d = wheel diameter, h = depth of sand, Os = precollapse structural cohesion, Ot = postcollapse structural cohesion, <^ = d3^namic postcollapse angle of internal friction, y = soil density, F = velocity of traction element of vehicle, g = gravity, ß — kinematic viscosity, / = friction between traction component and sand, S = slip ratio (ratio of speed of traction element to speed of advance of vehicle), B = parameter related to development of shearing resistance with deformation of sand, j = movement of traction element with respect to ground in one revolution of traction element (results from slip). By utilizing available knowledge equation 179 was simplified to

Many factors suspected to be of importance were eliminated from consideration when this was done, but their influence is apparently small so that practical relations result. By restricting considerations to sand and snow, equation 180 can be simplified even further. The angle of internal friction can be demonstrated to be essentially constant for sand and snow although difterent for each. Furthermore, maximum pull is usually generated at or near 25-percent slip in sand and snow. Thus, equation 180 is reduced to two Pi terms if pull at 25-percent slip is considered a measure ot performance. The only parameter that is difficult to measure is Os. If Cs could be suitably assessed and the other parameters experimentally measured, the two Pi terms D/W and W/Osd' should determine a unique SOIL DYNAMICS IN TILLAGE AND TRACTION 427 curve when plotted against each other. From this curve, the pull could be predicted for any vehicle whose gross weight and wheel diameter were known when a value for Cs (soil condition parameter) is determined. . ^ ^ ^ ^. In sand, the strength of soil varies with depth. Discussions m section 3.2.2.3 pointed out that the cohesion of soil could be increased by the application of forces as a result of induced strength. Whether the strength variation is induced by the dynamic action of loading a soil or whether the variation was originally present is immaterial; both affect traction. . The concept of relative cohesion offers a means for assessing the induced strength. A relative cohesion-plate size relation can be established for a soil condition in which a vehicle is to be operated by plotting Orel versus plate diameter from measured data of the form shown in figure 65. By assuming that the relative cohesion determined in a plate-soil system is the same as would appear m. a soil- vehicle system, the relative cohesion in a soil-vehicle system can be determined from a soil-plate system. In sand, a plate diameter ^5 the size of a tire diameter was arbitrarily assumed to predict the value of Orel' Grei for any soil-vehicle system can be determined from the experimentally determined relative cohesion-plate diameter curve. . T^- JÍ 4.- Eelative cohesion was used in the appropriate Pi term ot equation 180 and after some observation d^ was replaced by id (product o± width and diameter) so that the Pi term retained its dimensionless form. The pull of four-wheeled vehicles with all wheels powered (designated 4X4 vehicles) was measured over a period of 3 years (ñg. 291). Tire diameters ranged from 24 to 120 inches and wheel loads ranged from 50 to 50,000 pounds per wheel. The scatter band of points was not considered unreasonable in view of the variation m soil conditions one might expect in field situations. Figure 291 thus represents a traction equation that predicts the maximum pull ot 4X4 vehicles in sand.

~~0.6 • »~~

~~0.4 5ä^^==Z • »TÍ-~^. H ,~~

~~0.2~~

~~10 20 30 40 50 60~~

~~w c,bd~~

FIGURE 291.—Performance of 4 X 4 vehicles in sand. (Nuttall and McGowan at the Transportation Research Command ( 4^5 ). ) 428 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE A similar representation for 4 X 4 vehicles in snow was also developed when snow was restricted to dry tree-belt snow parks. While the relation is not completely accurate, figure 291 represents one of the more accurate traction prediction schemes available at this time. Because the total vehicle was considered and simplifications were made to eliminate several Pi terms, some inaccuracy probably should be expected. The traction mechanics discussed in section 7.2.2 has been used to derive traction equations. Harrison ( 176 ) used the Coulomb and Bernstein soil behavior equations as the basis for a mechanics. The developments reflected in equations 161, 162, and 163 and in figure 243 were modified slightly, but the principles were not changed. Traction equations for wheeled and tracked vehicles were developed. The equations were evaluated on a digital computer to avoid the cumbersome graphical procedures outlined in section 7.2.2. Slip-pull curves for the vehicles studied were measured experimentally and compared with the computed values. Figure 292 shows the comparison for a farm tractor in a Michigan

~~1500 fiD 1200~~

~~900 3 Û. 600~~

~~300 CALCULATED RANGE 0-, MEASURED .VALUES 10 20 30 40 50 60 70 80 SLIP (PERCENT)~~

FIGURE 292.—Calculated and measured pull of a farm tractor in a Michigan farm sou. (Harrison, 1st Internatl. Conf. Soil-Vehicle Systems Proc. {116).) farm soil. Other vehicles were also studied and the measurements and calculations repeated in a dry sand. The difference between calculated and measured pulls shown in figure 292 is typical of the difference in performance predicted for other vehicles in sand soil and is no greater than for any other prediction equation reported in the literature. The derived traction equation is the only scheme that attempts to consider slip. Since moré than the maximum pull is predicted, it is a more complicated scheme. More calculations and measurements are required to predict a pull, and the vehicle characterization is more complete in the derived scheme than the other empirically developed schemes. A traction equation based on a mechanics has the inherent means to fully represent all of the factors involved in traction. An SOIL DYNAMICS IN TILLAGE AND TRACTION 429 empirical traction equation does not inherently fully represent all factors affecting traction. New factors can be included only by modifying the equation. The accurate prediction of traction performance^ however^ is the ultimate goal and test of both approaches. 8. SOIL COMPACTION

8.1 Introduction In previous chapters, the complete scope of interest of soil dynamics—from descriptions of the soil through its behavior and use—has been developed. In agriculture, the compactness of soil affects the soil physical environment for crop production (S, 31, 52, 68, ISO, m m, 219, 257, 298, 299, 1,13, m, 516 ). Compaction reduces the soil s permeability to water, so that runoff and erosion may occur and adequate recharge of ground water is prevented. Compaction reduces aeration of the soil, so that metabolic activities of roots are hampered. Compaction increases the mechanical strength of the soil, so root growth is impeded. All of these effects may reduce the quality and quantity of food and fiber grown on the soil. Direct cause-and-effect relations appear to exist between the use of machinery and soil compaction, between soil compaction and a plant root environment, and between a plant root environment and crop production. These relations are qualitative, and intuition has led workers to try to directlv correlate the use of machinery with crop production. Because of the complexity of this machine-plant system, little progress has been made toward a solution. Less complicated systems must be analyzed to delineate the soil behaviors that describe and control subsystems wherein soil behavior has direct effect. When this is accomplished, information will be available to evaluate and control soil compaction in soil management systems. Two problems generally arise concerning soil compaction. Soil may be too compact to be used effectively in crop production. Pre- vention and alleviation of compactness are the problems associated with crop production. On the other hand, soil may not be compact enough to be used effectively for roads, dams, or building supports. Obtaining maximum compactness with minimum compacting effort is one of the problems associated with construction work. Soil compactness is a static state property of soil. Soil compaction changes the state of compactness. For a specific soil, the material properties generally do not change when the state of compactness is changed; only the static state changes. Since soil material and state properties determine behavior properties (sec. 3.1), a change m state of compactness indicates a probable change in behavior properties. Hence, regardles of its intended use, the soil is affected by compaction. General awareness of this fact has stimulated much soil compaction research. The goal of the research is to solve the two problems of compaction—to increase or decrease the state of compactness. Soil compaction is the action of soil becoming more compact. The action increases the state of compactness—actions that make soil 430 SOIL DYNAMICS IN TILLAGE AND TRACTION 431 less compact are normally not defined as soil compaction. Therefore, soil compaction is a d^rnamic soil behavior by which the state of compactness of soil is increased. Forces cause the action so that compaction behavior equations are required to describe the action. Forces that cause compaction originate from two general sources. Mechanical forces applied by machines and animals are one source ( 3, 257, 369 ). These forces are usually applied for short periods, and they can be measured without extreme difficulty. Natural phenomena are the second source of forces. For example, drying and other genetic processes cause soil compaction ( 166, 221 ). Natural forces usually operate for long periods, are difficult to define^ and have seldom been measured. Eegardless of the source, however, forces cause compaction. Compaction can occur only through movement of the soil itselt, and active behavior occurs. Accurate compaction behavior equations will provide a means to predict compaction. The ability to predict compaction is the first requirement for attaining control of compaction. Considerable research has been performed in attempts to develop soil compaction behavior equations. 8*2 Compaction Behavior Equations The inputs and outputs of compaction behavior relations are forces and changes in compactness, respectively. Eepresenting compaction behavior by an equation requires that both input and output be numerically described. Ideally, forces in soil should be defined by a stress tensor (sec. 2.2), which requires the measurement of six independent numbers. The compaction behavior input is more difficult to describe m numerical terms than the behavior output. The output can be expressed either as a change in the volume of the soil or as the absolute volume itself. Each measure of volume can be represented by a single number. Change in v^olume is the simpler output when the relation between input and output is linear or when the absolute volume has some constant base value at zero input. Since the observed soil compaction behavior does not exhibit either of these characteristics, absolute volume has been used as a numerical description of compaction behavior output. The state of soil compactness is expressed in several ways—bulk density (expressed on a wet or dry basis), void ratio, porosity, and apparent specific gravity. Definitions and references for standardized procedures of measurement were discussed in section 3.2.1.3. Methods were also described for simultaneously measuring stress and compaction; these can be used to study compaction behavior and develop behavior equations. Soil compaction can be considered as compression failure and representative of a yield criterion for soil. There are two types of compression failure. First, stress may cause compaction that is elastically recovered when the stress is removed. In other words, volume decreases as stress increases and volume increases as stress decreases {281). In principle, the compaction behavior output always follows the compaction behavior input. Mathematically, these input and output variables are uniquely related for all values over 432 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE their respective ranges. In the second type of compression failure, compaction is not recovered when the stress is removed. The compaction behavior output follows the compaction behavior input only when the input is above a threshold value and increasing. Mathe- matically, these input and output variables are not uniquely related for all values over their respective ranges; they are uniquely related only for a certain subset of the complete set of their values. The two types of compression failure are not unique to soil. Ductile materials are also designated as elastic or plastic, depending on whether strain is recoverable. The important point is that while both types are observed in soil, nonrecoverable compaction is much larger than recoverable compaction. Thus, nonrecoverable soil compaction is the type of compaction that is frequently studied. This behavior is rather special, since the input and output are uniquely related only for certain circumstances. These circumstances must be clearly recognized and understood in order to develop and interpret compaction behavior equations. Figure 293 shows the large amount of nonrecoverable soil com-

~~MOISTURE~~

~~HIWASSEE SANDY LOAM DAVIDSON CLAY~~

~~10 20 30 40 50 60 70~~

~~PRESSURE (LB./SO. FT.)~~

FIGURE 293.—Soil compaction resulting from applied forces. (Reaves, at the National Tillage Machinery Laboratory ( Sll ). ) paction behavior exhibited by loose unconsolidated soils. Forces were applied to a plunger acting on the open end of a cylindrical container filled with soil. The soil was confined and the compaction behavior input was expressed as the pressure applied to the soil by the plunger. Change in the volume of soil due to the plunger SOIL DYNAMICS IN TILLAGE AND TRACTION 433 movement was converted to dry bulk density, the compaction behavior output. Figure 293 illustrates three characteristics of compaction behavior. (1) Compaction behavior input and output are uniquely related, as the continuous curves indicate. But the relation holds only as long as the soil is not already consolidated and pressure is mcreasmg. Nonrecoverable compaction does not occur either when the pressure is reduced or when it is not large enough to cause additional nonrecoverable compaction. Thus, the curves in figure 293 represent the relation between input and output at incipient nonrecoverable compaction failure. (2) The large change of volume is a characteristic of compaction behavior. The change in the state of compactness ranges from 20 to 50 percent, depending on conditions. When maximum compaction is desired, forces of thousands of pounds are applied to produce even greater changes than shown m figure 293. (3) The moisture content of the soil affects compaction behavior. Each soil material was considerably more susceptible to compaction when it was wet. Equations describing the curves in figure 293 would be compaction behavior equations. If the equations could be sufficiently generalized, parameters would be available to represent the difference in shapes for various soils. Presumably these parameters could be related to the soil material and moisture content. Before undertaking such a task, however, some fundamental questions concerning compaction behavior must be answered. Soil m its natural environment generally is not confined; it exists as a semi-infinite three-dimensional medium. Furthermore, a compacting force is applied not over an entire area of soil but only over a small part of the area. Whether the compaction behavior studied m a confined container approximates the type of compaction that occurs in unconfined three-dimensional space may be questioned. Soehne ( 396 ) suggested an answer to the question. Since semi- infinite volumes of soil are loaded over small portions of their boundaries, distributions of forces must exist in the soil mass. Conse- quently, distribution of behavior inputs and outputs must exist m the soil mass. If the behavior of volume elements of soil could be described, a description of their distribution would permit predicting the compaction distribution. Six independent numbers define a stress tensor compacting a volume element of soil, but they are dependent on the choice of coordinate axes. An invariant (which is a combination of the six numbers and is independent of coordinate axes) or a combination of invariants thus must be used as the compaction behavior input. Soehne assumed that the largest principal stress uniquely caused soil compaction. The pressure applied to soil confined in a cylindrical container is the largest principal stress. If the container is shallow compared to its diameter, the vertical distribution of stresses within the soil will be small and the soil can be considered a volume element. Thus, compaction behavior as represented in figure 293 can be assumed to apply to a three-dimensional situation if the largest principal stress controls compaction. Considerable evidence now available indicates that the largest principal stress does not uniquely cause compaction. One of the 434 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE first indications was in data reported by Bodman and Eubin {48), They devised a soil-compacting apparatus that had a narrow, shallow annulus soil chamber. Soil was placed in the shallow annulus cham- l3er and loaded with a corrugated annulus ring that fitted closely mside the shallow chamber. The soil was confined and considered to behave as a volume element. Normal and tangential (shearing) forces were independently applied to the soil. The effects of normal and shearing stress on soil compactness are shown m figure 294. When only normal stress was applied, soil

~~O SHEAR BEGINS _2.0~~

E 3 1.6 ^-NORMAL LOAD .118 Kg/cm*

~~1.4 NORMAL LOAD .2Kg/cm2 ^SHEAR 1.2 1.0 ^NORMAL LOAD .737 Kg/cm* SHEAR üO.8 ^SHEAR~~

~~0.6 SHEAR T SPECIFIC VOLUME AT SATURATION 0.4 0.2 Q. < _L- -L. 100 300 500 700 900 100 200 300 400 TIME (sec) TIME (min)~~

FIGURE 294.—Effect of normal and shearing stress on compactness of soiL (Bodman and Rubin, Soil Sei. Soc. Amer. ( ^8 ).) compacted in the same manner as illustrated in figure 293. When shear was applied by rotating the corrugated loading ring (normal stress maintained constant), additional compaction occurred. Ap- plying both shearing and normal stresses to the surface of the soil not only increased the largest principal stress but also rotated its direction so that it was no longer perpendicular to the loading ring. They did not calculate the magnitude of the largest principal stress to determine whether a unique relation with specific volume existed, but they clearly demonstrated that shearing stress caused a significant amount of soil compaction. Additional evidence that the largest principal stress is not uniquely related to soil compaction was reported by Soehne, Chancellor, and Schmidt ( JfOJf ). They used lead shot to trace soil movement during compaction. A piston was forced into a box of uniformly packed soil. The soil and lead shot were X-rayed before and after loading. Superposition of the photographs permitted measuring the movements of the lead shot and the soil. Soil compaction could be calculated from the movements (fig. 295). The significance of figure SOIL DYNAMICS IN TILLAGE AND TRACTION 435

—I— mrnirnmiimii t I 12.5 K»/ciii*

~~FIGURE 295.—Lines of equal porosity (soil compaction) caused by a rigid plunger. (Soehne, Chancellor, and Schmidt, Amer. Soc. Agr. Engin. {hOk)-)~~

295 is that maximum compaction occurred at point x rather than immediately below the surface of the plunger. This same phenomenon was reported by Gill and Eeaves ( 160 ) under smooth tractor tires. The phenomenon can be explained if the largest principal stress is not uniquely related to soil compaction. In figure 295, point x is located at approximately the intersection of the 45° dotted lines subtended from the plunger. The area enclosed by the dotted lines and the face of the plunger represents a soil body (sec. 4.5.1) that acts as a portion of the plunger. Maxi- mum shearing strain occurs at the tip of the soil body because soil is forced to move around the body as it advances. Stresses in the soil at different distances from the plunger must either remain constant or decrease because only the plunger can originate forces applied to the soil. Hence the largest principal stress cannot be greater at point X than it is along the lower surface of the plunger. Since shearing strain was maximum at point x, and shear was demonstrated by Bodman and Eubin to cause compaction, maximum compaction at point X indicates that the largest principal stress is not uniquely related to compaction. Harris, Buchele, and Malvern ( 175 ) measured both the stress tensor and compaction on a volume element of soil. In previous work, the complete stress tensor was seldom measured. Bodman and Eubin measured the stresses on one surface of a volume element, but the stresses must be measured on three mutually perpendicular surfaces to determine the stress tensor. In making the measurements, Harris, Buchele, and Malvern ( 116 ) used a method suggested by Vanden Berg, Buchele and Malvern {1^59), In this method the principle of circular symmetry is used—that is, concentric circles located in horizontal planes below a circular load are subjected to the same state of stress. A concentric circle thus can be considered to represent a volume element of soil. Figure 296 shows the orienta- 436 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE LOAD

FIGURE 296.—Orientation of pressure transducers under a circular plate that will measure the stress tensor. (Harris, Buchele, and Malvern, Amer. Soc. Agr. Engin. (175 ).) tion of pressure transducers that permitted measuring the complete stress tensor. Soil-filled balloons were also placed on the circle, and compaction was measured by changes in volume after the manner of Hovanesian's volumeter method (fig. 20). Several invariants of the stress tensor, including the mean normal stress (equation 2) have been investigated by Vanden Berg, Buchele, and Malvern ( 4^9 ). They concluded that the mean normal stress may correlate better with compaction than the largest principal stress. The invariants were separately related to compaction for several soils in different conditions by Harris, Buchele, and Malvern ( 175 ). They concluded from a statistical comparison that all of the invariants indicated correlation. The maximum shearing stress had the largest coefficient of correlation although statistically it was no more significant than any other invariant. The use of circular symmetry has two difficulties: (1) the stress state cannot be carefully controlled, and (2) proportional loading is always present. Because of proportional loading, one invariant is always nearly directly proportional to any other invariant. Vanden Berg ( 457 ) used triaxial apparatus similar to that illustrated in figure 45 to overcome these difficulties. Stress states could be accurately controlled and widely varied. By using nonproportional loadings, the mean normal stress was increased while the largest principal stress decreased. Results showed that compaction always followed mean normal stress, whereas the largest principal stress could be decreased while compaction increased. Also, maximum shear stress had no correlation with compaction. The mean normal stress, however, did not uniquely correlate with compaction even though it was the best single invariant. SOIL DYNAMICS IN TILLAGE AND TRACTION 437 The effect of shear in compaction behavior was also studied. After the strain of the soil-volume element was measured, shearmg strain was calculated and expressed in the natural strain system (sec. 2.3). An expression was then empirically developed that related bulk density to mean normal stress plus the product of mean normal stress and maximum natural shearing strain. This relation is shown m figure 297 for several soils. A good correlation was obtained for all conditions except nonproportional loading. Even with nonproportional loading, however, the correlation predicted compaction with an error of less than 10 percent.

~~SANDY LOAM~~

~~1.6~~

~~1.5 CLAY ro E o 1.4 E~~

~~SILT LOAM t 1.3 zCO UJ Û 1.2~~

~~I.I OADING L LOADING~~

~~1.0 5 10 15 20 30 40 50 60~~

~~(^m+ ^m/max)~~

~~FIGURE 297.—Compaction relations for several soils. (Vanden Berg, Amer. Soc. Agr. Engin. ( ^57 ).)~~

The compaction relation shown in figure 297 is the most accurate available, but it is not very useful in its present form because both stress and strain must be measured to predict compaction. Since measurements of strain measure compaction directly, no need exists to predict compaction. The relation shows the importance of shear and demonstrates that no single invariant of the stress tensor controls compaction. Since shearing strain is caused by stress, the possibility exists of removing shearing strain from the input to compaction behavior by relating shearing strain to stress. 438 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE A number of factors have been studied with respect to their influence on soil compaction even though accurate compaction behavior equations do not exist. These studies serve to identify the general nature of compaction behavior. Hovanesian and Buchele (186) developed an apparatus (fig. 20) to study the effect of repetitive cycles of impact loads on soil compactness. A mean normal stress of 27 pounds per square inch was applied for 1 second followed by a rest stress of 1 pound per square inch. The stresses were controlled and pneumatically applied to a sealed chamber that contained balloon-enclosed soil samples. The duration of the load was approxi-

~~1 k 1.9~~

~~y"'^ SANDY LOAM 1.8 ■f1 "e 1.7 "1 ^O E o» 1.6 >- 1.5 ^ ¥^ SILTY LOAM ^ / 1.4 -/ M -J / 3 / CD 1.3 f 1.2 u.~~

~~0 5 K) 15 DUMBER OF IMRACTS~~

~~FIGURE 298.—Compaction of soil by repetitive loads. (Hovanesian and Bu- chele, Amer. Soc. Agr. Engin. Trans. ( 186 ).)~~

~~INSTRUMENTED^ DIAPHRAGM (PORE PRESSURE) OIL' FILLED OIL' FILLED X INSTRUMENTED CONNECTION POROUS STONE DIAPHRAGM (VERTICAL STRESS)~~

FIGURE 299.—Apparatus for measuring effective stress of saturated soil during impact loadings. (McRae, Northwestern Univ. {283).) SOIL DYNAMICS IN TILLAGE AND TRACTION 439 mately that applied by a driving wheel on an agricultural tractor. Figure 298 shows that compaction increased with each loading cycle, but from 70 to 90 percent of the total compaction occurred with the first impact. McKae ( 283 ) used a different technique to study compaction of saturated soil by impact loads. His apparatus (fig. 299) permitted measuring both pore pressure and total vertical stress. Effective stress is the algebraic difference between total stress and pore pressure. Two loadings were used: (1) A kneading load that resembled the action of a sheep's-foot packer and lasted for approximately 3 seconds, and (2) a falling weight impact load that lasted for 0.01 second. Typical examples of measured stress are shown in figure 300. Both effective stress, as a function of type of loading, and compaction were studied.

~~txJ DC~~

S I 295 lb/in* 130016/in*

~~^_A»ÊC—^ kl.01,«:~~

4 lb/In*

~~IMPACT KNEADING~~

~~FIGURE 300.—Curves showing stress measured during impact and kneading loads. (McRae, Northwestern Univ. {28S).)~~

Figure 301 shows the influence of moisture content on effective stress. Since all the soils were saturated, an increase in moisture content implies a more porous soil matrix. As the data indicate, increases in moisture content decreased effective stress. Since the applied stress was constant, the data imply that the stress carried by pore water increased as moisture content increased. Compaction was compared by noting the time required for the soils to reach equal densities. The impact load required approximately 0.4 second ; the kneading load required from 25 to 30 seconds. By varying time of loading, equal densities could be obtained with equivalent stress intensities. In other words, state of compactness was associated with level of stress, but the time required to obtain a state of compactness varied with the manner in which the stress was applied. Lewis ( 253 ) has also reported that loads applied by 440 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~400 r~~

~~_ 300 IMFÄCT (16 Ft. Lb.) Q.~~

~~<0 (O abJ 200 KNEADING (300 PSI)~~

~~KNEADING (200 PSI)~~

~~ï 100 -KNEADING (100PSI)~~

~~10 15 20 25 30~~

~~MOISTURE CONTENT (%)~~

FIGURE 301.—Influence of moisture content on the effective stress applied by impact and kneading loads. (McRae, Northwestern Univ. (283).) falling weights for 0.02 second were as effective in compacting soil as loads applied by rollers for 2 seconds. The importance of moisture content on compaction behavior was illustrated in figure 293. Its effect has been studied even though an accurate behavior equation has not been established. In lieu of a well-defined compaction behavior input, the input has often been expressed in terms of some constant compactive effort. Weaver and Jamison ( 498 ) used a modified Proctor procedure to study compaction. In the Proctor procedure, a hammer is dropped from a fixed height onto soil in a container. Figure 302 shows the effect of moisture on compaction of a clay loam soil. The compactive effort for the upper curve was twenty 12-inch blows of a 5.5-pound hammer to each of three 1%-pound layers of soils. The compactive effort for the lower curve was four 7-inch blows of a 5.5-pound hammer to each of the three 1%-pound layers of soil. The form of the curves indicates that the susceptibility of soil to compacting varies with its moisture content. The reduced compactibility (after point of maximum compaction is reached) reñects the effect of saturation. All voids in the soil are filled with water at saturation and water must be squeezed out of the soil as compaction occurs. A point of minimum compaction has also been reported by Rich- ards and others ( 366 ) for several other soil types. Thus the moisture content of a soil influences its susceptibility to compaction and, depending on moisture content, either a maximum or a minimum susceptibility can occur. Forces other than mechanical forces also cause soil compaction. Measuring these forces as inputs to compaction behavior relations is extremely difficult. Little progress has been made in developing SOIL DYNAMICS IN TILLAGE AND TRACTION 441

~~1.90~~

~~E ^1.80 É~~

~~^1.70 H~~

~~O) g 1-60 Û~~

~~§ 1.50 ^~~

~~1.40~~

~~"i 1 ' ^ 7Z 6 8 10 12 14 16 18 20 MOISTURE CONTENT (7o)~~

FIGURE 302.—Moisture-density relations of a clay loam soil for two levels of compactive effort. (Weaver and Jamison, Soil Sei. { 4^íi ).) behavior equations for forces of this type, usually the forces are not identified directly; rather, the cause of the forces is described. Dryins:, in which the action of soil compaction is termed shrinkage (fig. 303), is a typical force system of this type. Note that the behavior input is expressed as percentage of moisture loss and not absolute moisture content. The data indicate that compaction caused bv drying can be as great as that caused by mechanical torces. However, the losses for these soils (20 to 30 percent) require the input of significant amounts of drying energy. Usually moisture losses in soils are lower except at an exposed surface. Nevertheless, natural forces can cause excessive compaction and natural torce- compaction relations will have to be represented before compaction can be predicted and controlled. 8.3 Compaction in Tillage and Traction Soil compaction is important in tillage and traction because of its effect on the intended use of a soil. The consequences of compaction are of direct concern rather than compaction per se. These consequences are manifest in terms of specific active and passive behavior equations that are associated with use of the soil (sec. 6.2). Qualita- tive data that set limits on the desired state of compactness are available. Sufficient compactness to establish seed-soil contact and enhance germination is desirable in the immediate vicinity o± seed. Excessive compactness, on the other hand, is detrimental to maintaining a good root environment. Excessive compactness also reduces penetration of water and increases runoff and erosion. The intent is to control compaction during tillage and traction operations and to 442 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~10 15 20 25 30 35 WATER LOSS (%)~~

FIGURE 303.—Soil compaction caused by drying: A and B, two clay soils; C, a silt loam. establish or maintain soil in a suitable state of compactness for a specific use. The distribution of compaction is an important concern in the design and use of tillage and traction machines. Because the forces applied to soil by machines have not been described, empirical methods are used in the design of compaction machinery. Different machines are operated on soil, and the resulting compaction is measured ( £1, 33,38, 92,150, 263, 30i, m, W, ^79, 482 ). Distributions of compaction may be determined experimentally, but the qualitative nature of the results essentially precludes prediction of compaction in other situations. Section 8.2 pointed out that a soil compaction behavior relation and the compaction distribution must both be considered. Their interaction determines the state of compactness. Distribution of stresses is not peculiar to compaction. It also applies to the tillage and traction equations discussed in chapters 5, 6, and 7. These equations were presented without elaboration of possible distribution of initial and final soil conditions. Discussions here are restricted to distributions that occur in a plane perpendicular to a soil surface on which a tool or vehicle operates. Distributions of initial soil moisture and of compactness are usually found in the perpendicular plane. The simplified concepts discussed SOIL DYNAMICS IN TILLAGE AND TRACTION 443 in connection with the tillage and traction equations were adequate for nonvarying distributions. They are valid only for volumes of soil that represent volume elements. The description of distributions for use in tillage, traction, and compaction equations remains a problem. Presumably the simplest solution will be to include the distribution in the description of initial and final soil conditions. Distributions will be inherently described by a complete mechanics as the various equations are simultaneously considered, if a complete mechanics is ever developed. Since vehicular traffic often causes excessive soil compaction, studies have been made to measure distributions caused by different traction devices ( 196, J^l, Jf60, 485, 1^89, 4^7), In addition to density and porosity measurements, workers have used pressure transducers to measure force distributions under specific vehicles. Figure 304 m-

~~DEPTH BELOW SOIL SURFACE (INCHES) 0~~

~~I 2 3 4 5 6 DISTANCE - (FT.)~~

~~FIGURE 304.—Vertical stress distribution in soil under a tracked vehicle. (Cooper and Reaves, Fifth Internatl. Cong. Agr. Engin. (82).)~~

dicates the general stress pattern (82), The vibration or impact loads applied by rigid tracks produce peak stresses that are considerably higher than the average stress. Typical average ground pressures under this track are calculated to be 4 or 5 p.s.i. Keaves and Cooper ( 344 ) compared stress distributions under a single track and a pneumatic wheel (fig. 305). Each was loaded to 3,600 pounds and each was operated so that 1,500 pounds of pull was developed. The track was 12 inches wide and 5 feet long, and the wheel was a. 13-38 rubber tractor tire. The wheel caused greater 444 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~13-38 TIRE 12 I N. TRACK PS I~~

~~o 25~~

~~o 35~~

~~15 10 5 0 5 10 15 15 to 5 0 5 10~~

~~DISTANCE FROM CENTER LINE OF LOAD (IN)~~

~~FIGURE 305.—Mean normal stress under a track and a wheeL (Reaves and Cooper, Agr. Engin. ( SJfJf ).)~~

stresses at comparable depths so that the wheel caused more compaction than the track. The track applied a vibratory stress, whereas the pneumatic wheel applied a smooth stress. The wheel operated at a larger slip and imparted more shearing strain to soil. Thus, even though stress measurements are reasonably accurate, the stresses must be more completely defined and used with a compaction behavior relation before the distribution of compactness in soil can be predicted. In agricultural systems, excessive rather than inadequate compaction is generally the problem. Excessive compaction reduces the suitability of soil for crop production. Attempts have thus been made to relate state of compactness to plant growth. If such relations can be established, practical limits of permissible compaction can be determined. The influence of compaction on root penetration has been well studied {3, 298, 30i, I¡36, 516), Figure 306 shows how increased compaction may decrease root penetration. Root penetration could be retarded by several factors that are controlled by compaction ( 195, 377, ^23 ). Growth could be inhib- ited by mechanical resistance due to the strength of soil and by lack of air or water. Greacen ( 162 ) studied the interactions of soil strength, moisture tension, and void ratio for a clay soil (fig. 307). The angular strain is a common denominator against which to compare the effects of suction, shear strength, and compaction. Com- paction increased as the angular strain increased. Soil strength and moisture tension were increased as compactness increased. The void ratio is a measure of compactness, and the decreased void ratio indicates that less air space is available. Thus, as compactness in- SOIL DYNAMICS IN TILLAGE AND TRACTION 445

~~8 O.SOr~~

~~<--GALLION SILT LOAM~~

~~0.25 X lu t 0.00 8 »00 1.20 \30 L40 1.50 1.60 1.70 1.80 a: BULK DENSITY (gm/cm*)~~

FIGURE 306.—Effect of compaction on the penetration of sudangrass roots into cores of several soils. (Meredith and Patrick, Agron. Jour. (298).) creased, three important factors that affect plant growth changed in an undesirable manner so as to limit plant growth. Another indication of the effect of compaction on usefulness of soil was reported by Vomocil-, Fountaine, and Eeginato ( 4^7 ). They measured the rate at which water infiltrated soil before and after a tractor wheel had operated on the soil. Increases in drawbar pull were used as a means of increasing wheel slippage and increasing compaction. Figure 308 shows that the infiltration rate was reduced when soil compaction was increased by wheel slippage. A decreased water-infiltration rate of the soil usually increases water run-off and erosion, so that excessive compaction presents water and soil conservation problems. Soil compaction will receive increasing attention because it affects the suitability of a soil for an intended use. The economic importance of compaction varies because the value of soil is associated with use. Uses for soil continually change as man's needs change.

~~E u 800 t ñ 600~~

~~Z Ü 400 ^ hi~~

~~200~~

~~100 200 ANGULAR STRAIN (*»)~~

FIGURE 307.—Relations between soil strength, moisture tension, and void ratio as «oil compaction is varied. (Greacen, Internatl. Soc. Sei. Cong. Trans. (162).) 446 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

~~100 r~~

~~g 11 % MOISTURE CONTENT < z o ¡5 OC~~

~~500 1000 1500 2000 DRAWBAR PULL (lbs) (INCREASED WHEEL SLIP) ►~~

~~FIGURE 308.—The influence of wheel slip on infiltration of water in a loam soil at different initial moisture contents. (Vomocil, Fountaine, and Re- ginato, Soil Sei. Soc. Amer. (^67).)~~

Controlling compaction during tillage and traction is the goal. This control will require accurate stress-compaction behavior relations that can be described by equations. These remain to be developed. Once developed, a means for describing distributions of the state of compactness will be available. Only after these two entities can be numerically described will control of soil compaction be possible. In practice today soil compaction is controlled by the soil management system. A minimum-compaction soil management will increase intake of water, reduce erosion, increase aeration, and improve root penetration. Machine design and operation will have to be integrated into a workable soil management system before an optimum degree of compaction control can be attained. 9. SOIL DYNAMICS IN SOIL-MACHINE SYSTEMS

9.1 Systems Analysis Soil dynamics, as developed in this handbook, has been primarily concerned with a physical system composed of the soil and a machine. A machine may use the soil directly to serve some purpose such as traction; or a machine may manipulate soil to change its condition and thereby enable it to better serve some purpose—for example, plant growth. To evaluate a particular soil-machine system, the purpose for which the soil will be used must be considered. Almost without exception, the purpose for which soil is used involves a broader system of which the soil-machine system is only a subsystem. Thus, in evaluating a soil-machine system it must be considered in the context of the broader system. Methods for systems analysis will be required, particularly when the broader system is to be optimized. This chapter attempts to orient soil-machine sys- terms in broader systems and describe soil dynamics in such systems. A broad system can be evaluated if the various elements of the system can be quantitatively described, expressed in compatible terms, assigned relative weights of importance, and compared to standard requirements for the broad system. Unfortunately, in broad agriculturally or industrially oriented systems, various human, biological, economic, or agricultural policy elements cannot be quantitatively described. A major aim of research should be to develop the information required for quantitative description. Until this information is developed, two approaches exist for evaluating the performance of a system. First, the evaluation may be based on subjective determinations (by the evaluator) of how well a system meets arbitrary standards or requirements that the evaluator feels must be obtained by the system. Second, generalized techniques of evaluation that have been developed in areas presently identified as systems research, systems science, and systems engineering may be applied. The first approach has been widely used. Its success hinges on the skill and judgment of the evaluator and so is greatly influenced by the "human element." The second approach minimizes the influence of the human element and is more desirable. Five basic steps required for developing and using systems have been described by Eckman ( 109 ) and Hall ( 170 ) and have been applied to so-called loose systems. The five steps parallel those required for developing a rigorous mechanics. First, the problem must be defined so that it includes all factors that govern the relations of interest. Second, suitable objectives must be selected as goals to be obtained or as standards to be met. Third, systems are synthesized in the form of mathematical models that represent the 447 448 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE system of interest. Fourth, the system is analyzed by exploring the effect of alternate subsystems or of parameters in the subsystems on the desired or acceptable goals. Fifth, the most desirable system is then selected from the evaluation. When the degree of definition and representation of a system are good, the results of the evaluation will be definite. Conversely, when the representation is poor, the results will be indefinite. Any system consists of a hierarchy of contributing subsystems. The performance of the system is determined by the controlling elements of the subsystems. The accuracy of an expression of performance depends on two independent aspects, namely, the inclusion of all controlling elements and the accuracy of definition of each element (fig. 309). In figure 309, A represents a situation where a single element is precisely defined with a high degree of specificity. If the element is soil-metal friction, for example, it will not represent the performance of a soil-tillage tool system even if soil-metal friction is described with eight-place numerical accuracy. In situation B^ most of the elements are identified but none is described with sufficient accuracy to permit an accurate estimate of the performance of

~~CO O r=- > ÛL cc o CO LU Û~~

~~O h- O <~~

~~o >-~~

~~" i~~

~~FRACTIONAL COMPLETE COMPLETENESS OF REPRESENTATION~~

FIGURE 309.—Definition of soil-machine systems. SOIL DYNAMICS IN TILLAGE AND TRACTION 449 the system. Sandy soil and moldboard plow as a description of a soil-tillage tool system does not permit an aqcurate description of the performance of the system even though both subsystems are represented. In situation C both the accuracy of description and representation are sufficient to accurately describe the performance of the system. Most systems in which a soil-machine system is a subsystem are like situation B in figure 309. They are typical loose systems, where special techniques of systems analysis can be helpful. At present (1965), even soil-machine systems are largely loose systems. For- tunately, however, soil-machine systems are physical systems that can be more precisely described than can economic, social, or political systems. Most of the factors in soil-machine systems have been identified. The tillage equations in chapter 5 and traction equations in chapter 7 identify the abstract factors that control the systems. The problem is to increase the accuracy of the descriptions of these factors so that the equations do not represent generalized intuitive relations between abstract factors ; rather, they must represent specific relations between definite entities that can be identified by a number. With this information, performance of the soil-machine system can be predicted and controlled. Soil dynamics provides the concepts and framework so that the accuracy of the descriptions of the factors in a soil-machine system can be increased. Soil dynamics describes, and thus permits optimizing, the factors in a soil-machine system but has limited usefulness in other than a soil-machine system. As already pointed out, however, the soil- machine system is almost always a subsystem of a broader system. Soil dynamics will be useful in the broader system only insofar as the soil-machine system inñuences the broader system. The importance is illustrated in table 53 where a possible hierarchy of systems is shown for an agriculturally oriented system. The importance of soil dynamics ranges from one of interest to one of complete control, depending on the system that is considered. In a crop production system, for example, soil dynamics is important only insofar as the soil-machine system inñuences the performance of the broad system. If this inñuence is slight, the importance of soil dynamics will be slight. The correctness of the hierarchy of systems and controllmg subsystems selected in table 53 does not define the importance of soil dynamics in the various systems. Since no unique structure of matter has been absolutely defined, no absolute grouping of systems and subsystems can be defined. Presumably several hierarchies could be established for the same broad system, depending on how the subsystems are defined. Eegardless of the hierarchy, however, soil dynamics is centered in the soil-machine system and its use is restricted to that system. Thus, the bounds of applicability of soil dynamics are clearly established. Soil dynamics will become increasingly important in tillage and land locomotion in the future. The increasing world population will require a more thorough exploitation of land areas. While the uncertainties in land locomotion caused by Ü\^ soil can be removed by constructing durable road surfaces, it is neither possible nor desirable to build roads wherever man may travel. The results of re- 450 AGRICULTURE HANDBOOK 316, U.S. DEPT. OP AGRICULTURE

~~TABLE 53.—Soil dynamics as a disciplinée in the hierarchy of an agricultural system~~

Contributing ^ Importance of soil Scope of system subsystems dynamics as a discipline in broad systems 1. Crop production 2. Animal production- Individual farm- 3. Agricultural policy LSoil dynamics is of (price support and \ interest, production controls ) - .4. Marketing system— 1. Soil-machine ."^ Crop production 2. Soil-climate ] Soil dynamics influences system 3. Soil-plant _ > performance. 4. Plant-climate ^ Soil-machine system__. {1. Soil :5 Soil dynamics describes 2. Machine f system performance. A. Active behavior equa-^ Soil dynamics describes Soil-force system ) tion. / active and passive be- ]2. Passive behavior equa-j havior when soil is sub- tion. / jected to forces. il. Soil material proper- ") J ties. / Dynamic properties are Soil physical system- :S 2. Soil state properties ? determined by this (S. Soil behavior proper-] system, ties. '^ Soil material- (Molecular, atomic, and ) Basis of all physical ~\ subatomic factors. / systems. search in soil dynamics will be more fully exploited in agriculture, construction, mining, and exploration in order to improve the well- being of mankind. Thus, the soil will become an increasingly important medium on which to travel both on earth and on planets in outer space. Based on present knowledge (1965), basic principles developed for soils in this planet should also apply to soils of other planets. The extent to which the principles of soil dynamics will be developed and successfully used depends largely on future research. 9.2 Soil Dynamics as a Discipline The phenomena in the dynamic actions of soil and machines are so complex that they are difficult to study as complete systems. The need has thus arisen to break the overall actions down into simpler study units. However, these units may have interactions that cannot be studied in isolated systems. Isolated components, once evaluated, should be recombined as soon as possible so that the total system—rather than a series of smaller, simpler, nonrepresentative subsystems—is the subject of research. The foregoing chapters indicate that only a start has been made in obtaining the broad fundamental understanding that is required to adequately design and properly utilize tillage tools and traction or transport devices. From the several physical concepts that have SOIL DYNAMICS IN TILLAGE AND TRACTION 451 been identified, however, there has emerged a distinct area for research, study, and application. This area is soil dynamics. As was indicated earlier, this handbook is intended to bring together and analyze the diverse aspects of many seemingly heterogene- ous studies pertaining to soil dynamics for the purpose of establishing a coherent body of knowledge. As a newly defined area, soil dynamics must be fitted into the framework of present disciplines in order that its significance will become apparent. Figure 310 shows

~~PLANT REQUIREMENTS FROM SOIL~~

~~TRANSMITTED SUPPLIES OF AIR, HEAT, AND WATER~~

~~MECHANICAL SUPPORT, GROWING SPACE, LOW MECHANICAL IMPEDANCE~~

~~PREDOMINANT AREAS OF INTEREST ■■■■ SOIL GENESIS, PHYSICS ■■■ SOIL-MACHINE DYNAMICS FOR EACH DISCIPLINE • • • • SOIL PHYSICS !•■• SOIL PLANT DYNAMICS~~

FIGURE 310.—Soil dynamics as a discipline, and its association with plant growth. how soil dynamics is associated with plant growth. Figure 310 also shows that soil dynamics is a newly defined area or discipline concerning the dynamic action of the soil in tillage. The bulk of past work on soil mechanics has been associated with the needs of earth- work construction and foundations for large structures. As such, emphasis was placed on phenomena like the slow settling of soil under buildings—phenomena that are very different from the dynamic phenomena involved in vehicle mobility and tillage. Soil tilth also may evolve from genetic factors, but the active behavior of the soil under these forces is generally very slow. A second newly defined area is soil-plant dynamics. As m soil genesis, the active behavior of the soil is so slow that the force required to accelerate the soil is essentially zero during movement by plant roots. Not enough work has been done to define this area, but the scope and importance of the work is sufficient to warrant future development. . i • i i i • Soil physics as viewed here is generally associated with the physical transmission activities of the soil in which soil is passive. Prog- 452 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE ress in knowledge of soil physics has been largely in terms of transmission of soil moisture and soil air. Thus, if an area is recognized where the soil is active rather than passive, specialized courses can be taught and additional research can be directed toward obtaining basic knowledge concerning this important soil behavior. One final word can be said concerning soil dynamics. The farmer has effectively integrated soil relations in his system of interest by physical operations that are qualitative rather than quantitative; integration will not be as easy on a technical level. Kesearch generally develops information that separates into divergent areas of greater detail rather than into simpler and more complete bodies of knowledge. This handbook provides a framework m which the independent efforts of individual workers dealing with soil dynamics can be placed into perspective. Thus, even though some workers proceed into divergent areas in great detail, the relation and significance of the work can be realized and utilized by others. It is this realization that will provide common areas of interest for coordinating efforts in accepting and utilizing data from other sources. While some workers are developing narrow areas of application in detail, others may be unifying the problems of broader scope without mutual delay or interference. This unifying aspect of the organization of soil relations needs to be stressed in implementing all work in soil dynamics. Soil dynamics recognized as a discipline can serve this function. 9.3 Soil Dynamics and Tillage Tillage is defined as the physical manipulation of the soil; this definition is broader than the classical concept since it includes such operations as land forming, earth moving, and soil conditioning. These operations may be performed with the same tillage tools and in the same manner as classical tillage operations even though crop production is not contemplated. The fundamentals in the actions of various soil-machine systems are the same, and soil dynamics describes these actions. Hence, there is no need to restrict the field of application of soil dynamics to any specific purpose for the actions. The dynamic actions in soil-tillage tool systems are important because of the power used in tillage. McKibben ( 268 ) has calculated that for agriculture alone, 250 billion tons of soil are stirred or turned each year in the United States. This volume of soil represents a ridge 100 feet high and 1 mile wide extending from San Francisco to New York. To plow this ridge once requires 500 million gallons of gasoline. Even small savings of liquid fuels can be significant on a national basis. Energy savings may be influenced by factors other than those that govern the operating efficiency of a tillage tool itself. The efficiency of a tool operation can be increased only to the extent that the tillage objectives represent minimum energy requirements or expenditures. These objectives are determined by the requirements of the broad system in which the soil-tool system operates. A reflection on the tillage objectives that have been advocated in the past leads to the conclusion that a new philosophy of tillage is required. An acre of soil 6 inches deep weighs 2 million pounds. Plowing this acre SOIL DYNAMICS IN TILLAGE AND TRACTION 453 expends energy to move each furrow slice of soil laterally. Is this movement really necessary or is it a byproduct of our present-day techniques ? An equally astonishing example of wasted energy is the work expended to loosen an entire agricultural field only to follow this action by expending additional work to recompact most of the field. Ultimately, only a small fraction of the total field is planted. The American Indian's practice of using a small amount of tillage to place a fish and a seed in a hole is diametrically opposed to the present-day routine. Much of this apparently unnecessary tillage is actually harmful and goes undetected. One reason is the ease with which force can be applied to the soil with modern machinery. Machines can be operated at high speed and can apply great force to the soil without physical discomfort to the tiller. Thus, he is able to apply a large amount of energy to the soil in a short time without being aware that it may be excessive. The extent to which this practice has damaged the soil will never be known. Much has been made of the energy released on the soil by rain- storms and other natural forces. The sun alone releases 2 billion kilocalories of energy per acre per day ; but this energy is frequently dissipated in a shallow surface layer and any hardening or crusting at the surface can be removed with a small effort. The forces applied by machines are often large, and a high percentage of these forces compacts soil. Unfortunately, this compaction often extends several feet deep, and a large amount of work is required to remove the compaction. The elimination of undesirable forces in the first place will eliminate the secondary requirements for subsoiling and other forms of soil renovation tillage. Man with his machines is doing more damage to the soil in terms of plant requirements than nature can overcome. A second reason for unnecessary tillage may be the misguided pride of the tiller. A clean field has been considered the mark of a "job well done." This attitude results in tillage objectives that are pleasing to the eye even though they may not meet plant requirements. Finally, unnecessary tillage results from a fixed routine in tillage operations. The same series of operations is conducted year after year even though some of the operations are not needed. The realization that some conventional tillage is unnecessary is resulting in new practices to minimize the misuse of energy. Conduct- ing cultural operations from roadways, as practiced by the Hawaiian Pineapple Industry, is an example of a technique that minimizes traffic over soil. New so-called minimum tillage operations often till only the soil required for planting without concern about the remainder of the field. Since plant yields obtained by these practices are essentially the same as yields obtained by conventional practices, it would appear that some tillage as conventionally practiced is not necessary and that much energy may have been unnecessarily expended. . . Not all minimum tillage operations save energy. Some minimum tillage operations essentially combine all tillage tools normally used into a giant train. If the same soil manipulations are performed on the soil as are conventionally practiced, a reduction in the number of 454 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE trips over the soil does not necessarily constitute minimum tillage. A clear-cut example of minimum tillage is land forming. Com- puters have been used to calculate the minimum soil that needs to be moved to produce acceptable grades. By varying grades within prescribed limits, a smaller volume of soil needs to be handled. A sequence of tillage operations to achieve a desired soil condition is not a sacrosanct practice; rather, it is a necessity dictated by available tillage tools. The apparent philosophy guiding tillage tool design today is that each type of tool shall accomplish a specific action and that this action will be universally applicable. Such a philosophy is absurd since the soils and soil conditions that must be manipulated vary greatly. The tillage equations illustrate that the resulting soil condition is a function of the initial soil condition. For a constant shape and constant manner of movement (a universal tool), the resulting condition is determined by the initial soil condition ; it is not controlled by the tillage tool. If the resulting condition is not suitable, the tiller selects a different tool. Again, the resulting soil condition will be primarily determined by the condition before the operation, since shape and manner of movement are again constant. Because today's tiller has only limited control over the shape and manner of movement of a tool, he is forced to do sequence operations. Only by selecting different tools in a sequence can he change either the shape or the manner of movement or both, so as to produce the desired final soil condition. The present necessity of sequence operations can be avoided by two approaches. ^ Eliminating a sequence of operations means, in effect, that the soil will be manipulated to the desired condition in a one-step operation. Intuitively, proceeding from initial condition to final condition as directly as possible should require the least energy. Since many initial conditions will be encountered and many final conditions will be desired, many tool shapes and manners of movement will be required. For a specific situation, the tiller must have some means of selecting the combination of shapes and manner of movement that will accomplish the manipulation. He must have either a large number of shapes or a shape that he can vary and control. He must also have either a large number of mechanisms that will vary the manner of movement or one mechanism that he can vary and control. The two approaches for eliminating sequence operations thus are (1) a large number of tillage machines, each suitable for one specific circumstance; (2) a tillage machine that the tiller can adjust for a specific circumstance. A combination of the two possibilities may prove to be the practical solution. To give the tiller control over soil manipulation, tillage machines will have to become more complex ; simultaneously, the tiller will have to become a proficient technician, capable of properly using these machines. Other concepts of controlling soil conditions are possible. Little attention has been given to rocks and stones other than to remove them from the soil. With the advent of inexpensive yet powerful sources of energy, undesirable soil conditions may be corrected by a mechanical breakdown of particles in the soil large enough to hinder operations. On the other hand, artificial rocks could probably be SOIL DYNAMICS IN TILLAGE AND TRACTION 455 created if they are needed. It is conceivable that soil could be cemented and compressed into stable disks that would protect the surface from the climate and yet could be separated from root crops. If slowly soluble materials were used, they would gradually dissolve in a desired period of time. Thus, it appears that a new philosophy of tillage is needed. The establishment of realistic tillage requirements offers more possibilities for economy than does any other factor. Eliminating some of the operations now being conducted may be a greater saving than improving their efficiency. Establishing realistic tillage requirements is the first step in a system analysis. For soil-tillage tool systems, these requirements are determined by a broader system. Kegardless of the broader system and its specific requirements, in any soil-tillage tool subsystem the same type of information will be required. The type of information needed can be placed in four broad categories. First, the desired soil conditions must be known. Second, the existing soil conditions must be known. Third, the combinations of shape and manner of movement that can effect the required manipulation must be determinable. Fourth, the energy required to do the manipulation must be determinable. For a system analysis to be meaningful, each type of information must bß expressed in definitive and compatible terms. When fully developed, the concepts inherent m soil dynamics will provide the mechanism for definitive and compatible descriptions. Parameters of behavior equations provide the means of specitymg the first two categories. As was discussed in section 6.2, parameters of behavior equations quantitatively describe soil conditions in terms that are compatible with the intended use for a soil. Thus, regardless of the function of soil in a broad system, its desired condition can be defined by behavior parameters. Control of a desired soil condition by tillage stops as soon as the tillage is stopped. Natural forces continue to operate in, on, and around the soil and cause dynamic reactions. These forces are not controlled by tillage, and they may change soil conditions. In fact, a condition that is created by tillage may be so altered by a heavy rainfall that the effect of tillage is only momentary. Such considerations do not negate the concept of using behavior parameters to define soil conditions. Kather they illustrate the complexities m optimizing a broad system so that meaningful requirements can be assigned the soil-tillage tool subsystem. Soil dynamics as defined here does not include behavior resulting from natural forces. If these natural forces could be defined m the same way that mechanical forces can be defined, the present concepts of soil dynamics could be applied. Since natural forces cannot be so defined, soil dynamics is restricted to the soil-tillage tool subsystem and the bounds of its applicability are clear. The third and fourth categories of information are useful tor meeting the requirements placed on a soil-tillage tool subsystem. Concepts of soil dynamics provide the mechanism for defining and expressing the information. The tillage equations in chapter 5 are abstract expressions of the required information. Such equations 456 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE can be established by empirical means or by a rigorous mechanics. Concepts of soil dynamics provide the foundation on which research can be planned so that lacking information can be obtained. 9.4 Soil Dynamics and Traction Traction and transport vehicles that utilize rolling devices are the most widespread means of achieving land locomotion. Land locomotion can also be achieved by using devices that crawl, walk, or jump. Inherent in each act of locomotion, however, is some means for developing thrust from the ground media. When rolling takes place on rails, highways, or even crude roads, thrust and, consequently, locomotion itself can generally be predicted. In off-the-road movement, locomotion is highly unpredictable because of unpredictable soil conditions. Increased predictability of off-the-road movement is a goal to which the results of soil dynamics research can be applied. Land locomotion is a big business. It is important not only to the industry that produces traction and transport vehicles and to the users of these vehicles but also to the industry that supplies fuel. Farm tractors in the United States used 3.3 billion gallons of fuel in 1959. Each year at least 500 million tons of materials are transported from farms and ranches in the United States (268), Additional millions of tons of construction, mining, and military materials are moved by off-the-road vehicles. Any improvements that reduce direct operating costs will be of significant importance. Since traction IS widely used to transfer power to tillage tools, improvements that reduce operating costs become even more important. Locomotion with vehicles is almost universally achieved in off-the- road conditions. The soil and vehicle constitute a system, but this vehicle system is a subsystem of a broader system that provides the reason for or objective of the locomotion. It is in these broader systems that terms such as trafficability and mobility have been used. Usually these terms refer to the performance of the soil- vehicle system and imply a requirement of a broader system. The terms are often misleading; for example, soil trafficability when defined as "go" or "no-go" implies only that a soil can or cannot be traversed. When trafficability is further characterized by adverb modifiers such as easily, moderately, or with difficulty, time and cost considerations are also implied. Mobility performance is often expressed in equally ambiguous terms that also imply requirements of a broader system. For example, adequate mobility may imply the successful delivery of certain payloads under stringent conditions not imposed by the soil per se. Perhaps the most difficult problem in traction research has been the establishment of realistic performance requirements. One reason for the difficulty is the varied systems in which soil-vehicle systems are subsystems. Broadening the scope of systems places increasing requirements on the subsystems. Expressing these broad traction requirements in terms compatible with soil-vehicle systems is one bottleneck of traction research. Soil dynamics can be useful in eliminating the bottleneck by separating elements of traction performance from traction requirements. Thrust required and speed of movement are two factors basic to SOIL DYNAMICS IN TILLAGE AND TRACTION 457 all acts of locomotion. These two factors can be combined to express how much (thrust) and how quickly (speed) locomotion can be accomplished. The factors represent the functional contributions the soil-vehicle system makes to a broader system. Thus, with these factors and an expression for the energy required to achieve locomotion, the performance of the soil-vehicle system can be interpreted in any broad system. Economic or other considerations are determined by the broad system and not by the soil-vehicle subsystem. Thus, the requirement of any broad system can be made compatible with any soil-vehicle subsystem if the requirements are expressed in terms of thrust, energy, and speed. Soil dynamics is useful in developing the equations from either empirical measurements or analytical calculations. Thus soil dynamics in traction is analogous to soil dynamics in tillage. Knowledge of soil dynamics is centered in the soil-vehicle system and cannot be applied to actions beyond that system. Its influence in broader systems is only as important as the influence of the soil- vehicle system itself. Concepts of soil dynamics, if fully developed, provide a means for predicting and optimizing the performance of soil-vehicle systems. Full development of the concepts aivaits future research, but the direction in which the research should go is clearly established. Expressing the requirements of a broad locomotion system in terms of thrust, energy, and speed translates these requirements into specific soil-vehicle subsystem requirements that must be met. Categories of specific information needed to meet these requirements are, therefore, identified in a manner that is independent of any broad system. Specific items might include soil conditions to be traversed, geometry and flexibility of the traction devices on the vehicle, and the energy required to effect the locomotion. Soil dynamics knowledge is useful in quantitatively expressing the information and in predicting the performance the soil-vehicle system contributes to the locomotion system. As in tillage, soil dynamics does not determine the requirements of the system. The thrust available for locomotion is the net pull of a vehicle as determined by the combined pull of the traction device less the towing force of transport devices. Traction equations (ch. 7) express only the vehicle performance of soil-vehicle systems. Soil conditions can be expressed by behavior equation parameters for inclusion in the traction equations. The traction equations also describe the force requirements (torque) needed to effect traction. When speed is included in the equations, the energy requirements of the soil-vehicle system can be determined. 9.5 Conclusions Soil dynamics is a discipline concerning the study and application of soil-machine systems. When a soil-machine system is operating, the machine moves over or through the soil and the soil moves. Soil moves even though flexible components such as pneumatic tires apply the forces. Thus, soil movement is part of the action of any soil- machine system and soil dynamics describes both the movement of the soil and the interactions of the soil and a machine as a system. A soil-machine system is almost universally a subsystem of a 458 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE broader system of practical interest. The broad system determines the requirements that must be met by the soil-machine subsystem. These requirements not only are the objectives or goals of the subsystem; they also are the reason for the objectives. For example, a broad system determines the reason tillage is necessary as well as the goal that the tillage should accomplish. In addition to determining the requirements, the broad system determines the degree of importance of a soil-machine subsystem. This importance is proportional to the influence or control that the soil-machine system has in the action of the broad system. By describing (1) the movement of soil and (2) the interaction of soil on a machine as a system, soil dynamics provides the means for quantitatively describing the functional contribution of a soil-machine system to a broad system. In addition, soil dynamics provides the means for designing the soil- machine system so that it most effectively meets the requirements of the broad system. The soil dynamics discipline is not fully developed today. It is presently a discipline of concepts rather than of methods and solutions. Methods will be available and solutions will be possible when the discipline is fully developed. Present concepts are based on isolated bits of information from past research. These concepts cannot solve problems, but they do provide perspective in a nebulous system. This perspective is useful for five reasons: (1) It defines and delineates the soil dynamics discipline. (2) It shows how the elements of the discipline fit together. (3) It identifies the missing information that is a bottleneck in developing the discipline. (4) It provides guidelines for research that will develop the missing information. (5) It shows how the discipline can be applied to solve practical problems. That soil dynamics as a discipline can benefit man is clear, but it still must be suitably developed. The development awaits the highest degree of originality and ingenuity in research. Fortunately, new instrumentation, new techniques, and new knowledge are constantly becoming available. These new tools originate not only from soil dynamics research but also from other scientific endeavors of man. Miniaturization of transducers for industrial and national defense needs, development of computers for data analysis, and increased capability and sensitivity of electronic amplifiers are examples of improved instrumentation. These developments provide means for conducting research that was not possible a few years ago. Accelera- tion forces during soil movement, for example, have been measured by placing accelerometers in the soil during plowing ( 311 ). The technique provides a means for mapping the path soil travels as it moves over a tool. A number of workers have applied dimensional analysis and similitude procedures to soil dynamics research ( 30^ 35, 223, 308, 3I¡S, 4,25, JiS5, 505 ). New applications and improvements of the techniques themselves suggest that they will have increasing value in the future. But to benefit man, soil dynamics requires more than just developing the discipline. Soil dynamics is not implemented—if it is merely developed and stored on the shelves of reference libraries. It must be used. The usefulness of soil dynamics knowledge is twofold: (1) It SOIL DYNAMICS IN TILLAGE AND TRACTION 459 provides a means fof predicting performance of soil-machine systems. (2) It provides a means for designing a soil-machine system so that a desired performance can be attained. Inherent in design is the concept of attaining optimum or maximum efficiency. Generally, a specific performance can be obtained in more than one way. For example, a soil manipulation can probably be effected with several combinations of tool shapes and manners of movement. Techniques will be needed to optimize the performance of soil- machine systems. Systems analysis (discussed brieñy in sec. 9.1) is one technique that will be useful. In particular, systems analysis will be useful durmg the development of soil dynamics, when it may be classified as a loose system. Other techniques are also available. Linear program- ing and response surface techniques have been developed and used in economic and industrial management problems ( P7, 116^ 165). These techniques should also be applicable to practical soil dynamics problems. Analogs provide another useful technique. They may be physical ( 26, Uh ^^. ^U, SJß, 383, 433, m ) so that a system can be studied, or they may only simulate the behavior of the system (^7,^5^). When a soil-machine system can be synthesized with equations, analog and digital computers can be used to optimize a specific problem. Thus, no major obstacle appears to exist to prevent applying soil dynamics to practical problems. Man has lived on land for many years and he will continue to do so. During past years he has made much progress and has learned to use land without a formal discipline of soil dynamics. A critical analysis of man's present utilization of land shows that he employs qualitative, intuitive methods implemented by machines varying in complexity from hand-powered to highly-mechanized. These methods "get the job done" but they do not permit control over what is done. To obtain control, qualitative and intuitive methods must be replaced by quantitative, exact methods. The concepts of soil dynamics provide the means for making the transition. The challenge is to fully develop the soil dynamics discipline so that better control and use of land can be obtained. 10. SELECTED REFERENCES

A few of the following references are not readily available in all agricultural libraries. Assistance in locating specific references can be obtained from the National Tillage Machinery Laboratory, Auburn, Ala.

(1) ADAMS, W. J. and FURLONG, D. B. 1959. ROTARY TILLER IN SOIL PREPARATION. Agr. Engin. 40 I 600-603, 607, iUus. (2) ALLISON, R. 1923. THE MODULUS OF RUPTURE OF SOIL AS AN INDEX OF ITS PHYSICAL STRUCTURE. Agron. JouF. 15: 409-415, iUus. (3) AMERICAN SOCIETY OF AGRICULTURAL ENGINEERS. 1959. ANNOTATED BIBLIOGRAPHY ON SOIL COMPACTION. 31 pp. Amer. Soc. Agr. Engin. St. Joseph, Mich. (4) AMERICAN SOCIETY OF AGRICULTURAL ENGINEERS-SOIL SCIENCE SOCIETY OF AMERICA. 1958. CONCEPTS, TERMS, DEFINITIONS AND METHODS OF MEASUREMENT FOR SOIL COMPACTION. Agr. Engin. 39: 173-176. (5) AMERICAN SOCIETY OF AGRONOMY. 1952. SOIL PHYSICAL CONDITIONS AND PLANT GROWTH. MonOgraph, V. II, 491 pp., illus. New York. (6) 1957. DRAINAGE OF AGRICULTURAL LAND. Monograph v. VII, 620 pp., iUus. Madison, Wis. (7) AMERICAN SOCIETY OF CIVIL ENGINEERS. 1960. RESEARCH CONFERENCE ON SHEAR STRENGTH OF COHESIVE SOILS. 1164 pp., iUus. New York. (8) AMERICAN SOCIETY FOR METALS. 1961. METALS HANDBOOK. Ed. 8, V. I, iUus. Novelty, Ohio. (9) AMERICAN SOCIETY FOR TESTING MATERIALS. 1947. SYMPOSIUM ON LOAD TESTS OF BEARING CAPACITY OF SOILS. Spec. Tech. Pub. 79, 148 pp., iUus. Philadelphia. (10) 1950. SYMPOSIUM ON THE IDENTIFICATION AND CLASSIFICATION OF SOILS. Spec Tech. Pub. 113, 91 pp., iUus. Philadelphia. (11) 1951. SYMPOSIUM ON CONSOLIDATION TESTING OF SOILS. SpCC. Tcch Pub. 126, 109 pp., illus. Philadelphia. (12) 1952. SYMPOSIUM ON DIRECT SHEAR TESTING OF SOILS. SpCC. Tcch Pub. 131, 87 pp., iUus. Philadelphia. (13) 1953. DYNAMIC TESTING OF SOILS. Spcc. Tech. Pub. 156, 261 pp., illus. Philadelphia. (14) 1958. PROCEDURES FOR SOIL TESTING. 544 pp., illus. Philadelphia. (15) 1959. SYMPOSIUM ON PARTICLE SIZE MEASUREMENT. Spec. Tech Pub. 234, 318 pp., nius. Philadelphia. (16) 1961. SYMPOSIUM ON SOIL DYNAMICS. Spcc. Tech. Pub. 305, pp., illus. Philadelphia. 460 SOIL DYNAMICS IN TILLAGE AND TRACTION 461

(17) ARYA, S. V., and PICKARD, G. E. 1958. PENETRATION OF LIQUID JETS IN SOIL. Agr. Engin. 39: 1^ 19, 23, illus. (18) ASHBY, W. 1931. A METHOD OF COMPARING PLOW BOTTOM SHAPES. Agr. Engin. 12: 411-412, illus. (19) 1929. PROGRESS REPORT ON PLOW INVESTIGATIONS. U.S. Dcpt. Agr. Bur. Public Roads, Div. Agr. Engin. Rpt., 65 pp., illus. (20) ATTERBERG, A. 1912. DIE KONSISTENZ UND DIE BINDIGKEIT DER BODEN. lutematl. Mitt. f. Bodenk. 2: 149-189, illus. (21) ATTWOOD, P. R. 1957. SOME EFFECTS OF SPEED ON THE EFFICIENCY OF ROLLING. JOUR. Agr. Engin. Res. 2: 217-221. (22) BAADER, W. 1961. [THE SEPARATION OF SOIL IN POTATO DIGGERS EQUIPPED WITH OSCILLATING SIEVES.] Landtechnische FoTsch. (Munich) 11: 160-165, illus. (23) BACON, C. A. 1920. A TREATISE ON PLOWS AND PLOWING. Ed. 2, 200 pp., illUS. South Bend, Ind. (24) 1929. SOME PHYSICAL ASPECTS OF ORGANIC MATTER. Agr. Eugiu. 10: 83-85, illus. (25) BAILEY, P. H. 1956. THE COMPARATIVE PERFORMANCE OF SOME TRACTION AIDS. JOUr. Agr. Engin. Res. 1: 12-22, illus. (26) FiLBY, D. E., and TáLAMO, J. D. C 1961. PRELIMINARY EXPERIMENTS WITH A METHOD OF SIMULATING A SOIL WITH CONTROLLABLE SHEAR STRENGTH. Jour. Agr. Engin. Res. 6: 222-224, illus. (27) BAINER, R., KEPNER, R. A. and BARGER, E. L. 1955. PRINCIPLES OF FARM MACHINERY. 571 pp., illus. New York. (28) BAKHTIN, P. U. 1954. [DYNAMICS OF THE PHYSICO-MECHANICAL PROPERTIES OF SOIL IN CONNECTION WITH QUESTIONS OF CULTIVATION.] PochveU. Inst. Im. Dokuehaeva [Leningrad] Trudy. 45: 43-215, illus. (29) BARGER, E. L. CARLETON, W. M., MCKIBBEN, E. G., and BAINER, R. 1952. TRACTORS AND THEIR POWER UNITS. 496 pp., iUus. New York. (30) BARNES, K. K., BOCKHOP, C. W., and MCLEOD, H. E. 1960. SIMILITUDE IN STUDIES OF TILLAGE IMPLEMENT FORCES. Agr. Engin. 41: 32-37, 42, illus. (31) BATEMAN, H. P. 1954. EFFECTS OF BASIC TILLAGE METHODS AND SOIL COMPACTION ON CORN PRODUCTION. 111. Agr. Expt. Sta. Bui. 654, 35 pp., illus. (32) BAVER, L. D. 1956. SOIL PHYSICS. Ed. 3, 489 pp., illus. New York. (33) BECKER, C. F. 1959. SOIL COMPACTION PRESSURES UNDER ROLLING PRESS WHEELS. Amer. Soc. Agr. Engin. Trans., 2: 63-64, 67, 70, illus. (34) BEKKER, M. G. 1957. INTRODUCTION TO RESEARCH ON VEHICLE MOBILITY. Part 1. Land Locomotion Lab. Rpt. 22, 126 pp., illus. (35) 1957. THEORY OF LAND LOCOMOTION. 520 pp., illus. Ann Arbor, Mich. (36) 1958. PERFORMANCE IMPROVEMENT IN TRACK-TYPE TRACTORS. Agr. Engin. 39: 630-632, illus. (37) 1960. OFF THE ROAD LOCOMOTION, 220 pp., illus. Ann Arbor, Mich. (38) BERNHART, R. K. 1952. STATIC AND DYNAMIC SOIL COMPACTION. Highway Res. Board Proc. 31: 563-592, illus. 462 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

(39) BERRY, M. O. 1948. COULTER TESTS. U.S. Tillage Mach. Lab. (Auburn, Ala.) Ann Rpt. (40) BERTELSEN, W. R. 1960. THE AEROMOBILE : A PERIPHERAL JET VEHICLE. AffF. Engin 41 * 290-292, illus. (41) 1960. SOMETHING BRAND NEW IN PLOWS THE AEROPLOW. DeS Moines Register. Aug. 21, Sect. H, p. 17-H. (42) BiGSBY, F. W. 1961. EFFECT OF AN AIR FILM ON SOIL TO TILLAGE SURFACE FRICTION. Ph.D. thesis. Iowa State Univ., 85 pp., illus. (43) BiKERMAN, J. J. 1958. SURFACE CHEMISTRY. Ed. 2, 501 pp., illus. New York (44) BJORCK, G. 1958. STUDIES ON THE DRAUGHT FORCE OF HORSES. Acta Agr. Scand. Sup. 4, 109 pp., illus. (45) BOA, W. 1958. DEVELOPMENT OF N.I.A.E. DITCH CLEANER. Jour. AsT Engin Res. 3: 17-26, illus. (46) and WHYTE, P. 1960. THE DESIGN OF A PLOUGH FOR LAYING UNDERGROUND CABLES. Jour. Agr. Engin. Res. 5: 135-140, illus. (47) BODMAN, G. B. 1949. METHODS OF MEASURING SOIL CONSISTENCY. Soll Sci 68* 37- 56, illus. (48) and RUBIN, J. 1948. SOIL PUDDLING. Soil Sci. Soc. Amer. Proc. 13: 27-36 illus (49) BONMARTINI, G. ' 1961. THE WHEEL: ROADS—THE TRACKS: NATURAL SOILS. 272 pp. illus. Rome. ' (50) BowDEN, F. P., and TABER, D. 1950. THE FRICTION AND LUBRICATION OF SOLIDS. 337 pp., illuS. Oxford. (51) BowEN, H. D. 1960. SOME PHYSICAL IMPEDANCE AND AERATION EFFECTS ON PLANTED ,^^, ^ SEEDS. Amer. Soc. Agr. Engin. Paper 60-626, 19 pp., illus. (52) BoYD, M. M. 1959. COMPACTION AND SLIPPAGE EFFECTS OF FORAGE HARVESTING MACHINERY. Amer. Soc. Agr. Engin. Paper 59-102, 7 pp illus. (53) BROWNING, G. M. 1950. PRINCIPLES OF SOIL PHYSICS IN RELATION TO TILLAGE Affr Engin. 31: 341-344. (54) BRUCE, R. R. 1955. AN INSTRUMENT FOR THE DETERMINATION OF SOIL COMPACTI- ,^^, BiLiTY. Soil Sci. Soc. Amer. Proc. 19: 253-257, illus. (55) BRU WER, J. J. 1962. THE INSTANTANEOUS TRACTIVE EFFICIENCY OF A 12-38 PNEU- MATic TRACTOR TIRE. Amer. Soc. Agr. Engin. Trans. 5: 114. (56) BUSCH, C. D. 1958. LOW COST SUBSURFACE DRAINAGE. Agr. Engin. 39: 92-93 97, 103, illus. * ' (57) 1958. MECHANICAL MOUSE AIDS RESEARCH IN SUBSURFACE DRAINAGE Agr. Engin. 39: 292-293, illus. (58) CAREW, N. /^^^ •^^^^* ®^^^ COMPACTION. Sugar Jour. 18: 35-38, illus. (59) CARLETON, W. M., and MARTIN, J. W. 1945. SHARPENING AND HARDSURFACING PLOW AND LISTER SHARES Kans. Engin. Expt. Sta. Bui. 44, 40 pp., illus (60) CARLSON, E. C. 1961. PLOWS AND COMPUTERS. Agr. Engin. 42: 292-295, 307, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 463

CABNES, A. 1934. SOIL CRUSTS METHODS OF STUDY, THEIR STRENGTH, AND A METHOD OF OVERCOMING THEIR INJURY TO COTTON STAND. Agr. Engin. 15: 167-171, illus. CARPENTER, F. G., and DEITZ, V. R. 1951. GLASS SPHERES FOR THE MEASUREMENT OF THE EFFECTIVE OPENING OF TESTING SIEVES. [U.S.] Nat'l. Bur. Standards Jour. Res.. 47 : 139-147, illus. CASAGRANDE, A. 1947. CLASSIFICATON AND IDENTIFICATION OF SOILS. AMER. SOC. Civ. Engin. Proc. 73: 783-810, illus.

1955. LABORATORY INVESTIGATIONS OF THE EFFECTS OF ELECTRO-OS- MOSIS ON FINE-GRAINED SOILS. Soil Mech. Lab., Harvard Univ. Rpt. to Bur. Yards and Docks, illus. CEGNAR, A., and FAUSTI, F. 1961. MOVEMENTS UNDER THE CONTACT AREA OF RADIAL AND CON- VENTIONAL TIRES. Amer. Soc. Agr. Engin. Trans., 4: 224- 225, illus. CHANCELLOR, W. J., and SCHMIDT, R. H. 1962. A STUDY OF SOIL DEFORMATION BENEATH SURFACE LOADS. Amer. Soc. Agr. Engin. Trans. 5: 240-246, 249, illus. CHASE, L. W. 1942. A STUDY OF SUBSURFACE TILLER BLADES. Agr. Engin. 23: 43- 45, 50, illus. CHEMICAL RUBBER PUBLISHING COMPANY. 1950. HANDBOOK OF CHEMISTRY AND PHYSICS. Ed. 32, 2879 pp. Cleveland. CHEPIL, W. S. 1951. AN AIR ELUTRIATOR FOR DETERMINING THE DRY AGGREGATE SOIL STRUCTURE IN RELATION TO ERODIBILITY BY WIND. Soil Sci. 71: 197-207, illus.

~~1951. IMPROVED ROTARY SIEVE FOR MEASURING STATE AND STABILITY OF DRY SOIL STRUCTURE. Soil Sci. Soc. Amer. Proc. 16: 113- 117, illus.~~

~~1951. PROPERTIES OF SOIL WHICH INFLUENCE WIND EROSION : V. MECHANICAL STABILITY OF STRUCTURE. Soil Sci. 72: 465-478, illus.~~

1958. SOIL CONDITIONS THAT INFLUENCE WIND EROSION. U.S. Dept. Agr. Tech. Bui. 1185, 39 pp., illus. WOODRUFF, N. P., SIDDOWAY, F. R., and LYLES, L. 1960. ANCHORING VEGETATIVE MULCHES. Agr. Eugiu. 41: 754-755, 759, illus. CHILDS, E. C. 1955. THE PHYSICAL ASPECTS OF SOME CONCEPTS IN SOIL MECHANICS. Nati. Acad. Sei. Proc. (India) 24A: 86-92, illus. CLYDE, A. W. 1936. MEASUREMENT OF FORCES ON TILLAGE TOOLS. Agr. EugiU. 17 : 5-9, illus.

~~1937. LOAD STUDIES ON TILLAGE TOOLS. Agr. Eugiu. 18: 117-121, illus.~~

~~1944. TECHNICAL FEATURES OF TILLAGE TOOLS. Pa. Agr. Expt. Sta. Bui. 465, 40 pp., illus. COHRON, G. T. 1961. MODEL TESTING OF EARTHMOVING EQUIPMENT. Amer, SOC. Agr. Engin. Paper 61-113, 4 pp., illus.~~

~~1963. SOIL SHEARGRAPH. Agr. Engin. 44: 554-556. 464 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE~~

(80) COMMONWEALTH SCIENTIFIC and INDUSTRIAL RESEARCH ORGANIZATION. 1960. INTERP ARTICLE FORCES IN CLAY-WATER-ELECTROLYTE SYSTEM. Univ. of Melbourne, Australia, illus. (81) COOPER, A. W., and MCCREERY, W. F. 1961. PLASTIC SURFACES FOR TILLAGE TOOLS. Amer. Soc. Agr Engin Paper 61-649, 8 pp., illus. (82) and REAVES, C. A. 1960. STRESS DISTRIBUTION IN THE SOIL UNDER TRACTOR LOADS. Fifth Internatl. Cong. Agr. Engin. 1958 Trans. (Brussels) 2: 1190-1198, illus. (83) VANDEN BERG, G. E., MCCOLLY, H. F., and ERICKSON, A. E. 1957. STRAIN GAGE CELL MEASURES SOIL PRESSURE. Agr Engin 38: 232-235, 246, illus. (84) CORLEY, T. E. 1949. AN ANALYSIS OF A MOLDBOARD PLOW SURFACE FOR THE PURPOSE OF IMPROVING ITS PERFORMANCE. M. S. Thesis, Aubum Univ., 34 pp., illus. (85) CowiN, S. C. KONDNER, R. L., and AYRE, R. S. 1958. BIBLIOGRAPHY RELATING TO VIBRATORY CUTTING, PENETRATION AND COMPACTION OF SOILS,. Tech. Rpt. 2 by Johns Hopkins Univ. to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss., 37 pp. (86) KoNDNER, R. L., and AYRE, R. S. 1958. BIBLIOGRAPHY RELATING TO VIBRATORY CUTTING, PENETRATION, AND COMPACTION OF SOILS. Supp. 1, Tech. Rpt. 3 by Johns Hopkins Univ. to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss., 34 pp. (87) KoNDNER, R. L., and AYRE, R. S. 1958. A CRITICAL REVIEW OF SELECTED LITERATURE RELATING TO THE VIBRATORY CUTTING, PENETRATION, AND COMPACTION OF SOILS. Tech. Rpt. 4 by Johns Hopkins Univ. to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss., 40 pp (88) CRONEY, D., and COLEMAN, J. D. 1954. SOIL STRUCTURE IN RELATION TO SOIL SUCTION (üF) Jour Soil Sei. 5: 75-84, illus. (89) CROWTHER, E. M., and HAINES, W. B. 1924. AN ELECTRICAL METHOD FOR THE REDUCTION OF DRAFT IN PLOW- ING. Jour. Agr. Sei. 14: 221-231, illus. (90) CULPIN, C. 1937. STUDIES ON THE RELATION BETWEEN CULTIVATION IMPLEMENTS, SOIL STRUCTURE AND THE CROP. III. ROLLS: AN ACCOUNT OF METHODS EMPLOYED IN A STUDY OF THEIR ACTIONS ON THE SOIL. Jour. Agr. Sei. 27: 432-446. illus. (91) CYKLER, J. F., and TRIBBLE, R. T. 1961. PRINCIPLES OF INJECTION SOIL FUMIGATION. Amer Soc Agr Engin. Trans., 4: 199-202, illus. (92) DADAEV, G. T. 1958. [RAMMING ROLLER FOR SOIL COMPACTION.] Gidrotekhnika Me- lioratsiya [Moscow] 10(31) : 18-25, illus. [Off. Tech Serv Eng. Translation, 60-21158.] (93) DANO, P. L. 1961. THE INFLUENCE OF SOIL CONDITIONS ON THE EFFECTIVENESS OF ELECTRO-OSMOSIS AND TEFLON IN REDUCING SLIDING FRICTION M. S. Thesis, Auburn Univ., 115 pp., illus. (94) DAVIDSON, J. B., and COLLINS, E. V. 1929. THE DIRECT APPLICATION OF MECHANICAL POWER TO SOIL TIL- LAGE. Agr. Engin. 10: 165-168, illus. (95) COLLINS, E. V., and MCKIBBEN, E. G. 1935. TRACTIVE EFFICIENCY OF THE FARM TRACTOR. lowa Agr EXDt sta. Res. Bui. 189, pp. 258-333, illus. (96) and MCKIBBEN, E. G. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. X. THE VALUE AND COST OF PNEUMATIC TIRES. Agr. Engin. 21 * 319- 321, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 465

DAVIES, D. L. 1954. THE DESIGN AND ANALYSIS OF INDUSTRIAL EXPERIMENTS. 636 pp., illus. London and Edinburgh. DAVIS, W. M. 1961. IMPLEMENT REQUIREMENTS IN RELATION TO TRACTOR DESIGN. Agr. Engin. 42: 478-483, illus. DAY, P. R.. 1950. PHYSICAL BASIS OF PARTICLE SIZE ANALYSIS BY THE HYDRO- METER METHOD. Soil Sei. 70: 363-374, illus. and HOLMGREN, G. 1952. MICROSCOPIC CHANGES IN SOIL STRUCTURE DURING COMPRESSION. Soil Sei. Soe. Amer. Proc. 16: 73-77, illus. DELEENHEER, L., and DEBOODT, M. 1958. DETERMINATION OF AGGREGATE STABILITY BY THE CHANGE IN MEAN WEIGHT DIAMETER, Intomatl. Syuipos. OU Soil Struc- ture Proe. (Ghent, Belgium) pp. 290-300, illus. DICKSON, W. J. 1962. GROUND VEHICLE MOBILITY ON SOFT TERRAIN. AMER. SOC. CIV. Engin. Proc. 88 (SM4, pt. 1) : 69-83, illus. DiNGLINGER, E. 1932. THE CUTTING OF SAND. Engineering 134: 116-118. DOMSCH, M. 1955. [PROBLEMS OF SOIL CULTIVATION.] 140 pp., illus. Berlin. DONER, R. D. 1936. A THEORY OF ARCH ACTION IN GRANULAR MEDIA. Agr. Eugiu. 17: 299-304, illus. and NICHOLS, M. L. 1934. THE DYNAMIC PROPERTIES OF SOIL. V. DYNAMICS OF SOIL ON PLOW MOLDBOARD SURFACES RELATING TO SCOURING. Agr. Engin. 15: 9-13, illus. DUBROVSKII, A. A. 1956. [INFLUENCE OF VIBRATING THE TOOLS OF CULTIVATION IMPLE- MENTS UPON DRAFT RESISTANCE.] Vsesoiuzz. Akad. Scl' skok- hozhaistvenny k h Nauk. Zeml. Mekh. Shorn. Trudov. (Leningrad) 3: 182-185, illus. [Nati. Inst. Agr. Engin., Eng. Translation 51.] Dupuis, H. 1959. EFFECT OF TRACTOR OPERATION ON HUMAN STRESS. Agr. EugiU. 40: 510-519, 525, illus. ECKMAN, D. P. 1960. SYSTEMS : RESEARCH AND DESIGN. 310 pp., illus. New York. EGGEN MÜLLER, A. 1958. [OSCILLATING IMPLEMENTS : KINEMATICS AND EXPERIMENTS WITH MODELS.] Grundlagen der Landtechnik 10: 55-69, illus.

1958. [FIELD EXPERIMENTS WITH AN OSCILLATING PLOW BODY.] Grundlagen der Landtechnik 10: 89-95, illus. ELIEZER, J. C. 1946. ON DIRAC'S THEORY OF QUANTUM ELECTRODYNAMICS. Roy. Soc. London, Proc, Ser. A, 123: 197-210, illus. EVANS, I., and SHERRATT, G. G. 1948. A SIMPLE AND CONVENIENT INSTRUMENT FOR MEASURING THE SHEARING RESISTANCE OF CLAY SOILS. Jour. Sei. Inst. 25 : 411-414, illus. FAIRBANKS, G. E. 1961. WEAR RESISTANCE OF TILLAGE TOOLS CUTTING EDGES. Amer. SOC. Agr. Engin. Paper 61-122, 10 pp., illus. FARMING MECHANIZATION. 1962. Shin Norin Co., Ltd., Tokyo. FiCKEN, F. A. 1961. THE SIMPLEX METHOD OF LINEAR PROGRAMMING. 58 pp. NcW York. FISCHER, J. J. 1960. SOLID-SOLID BLENDING. Chcm. Eugiu. 67: (17) 107-128, illus.

~~K 466 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE~~

(118) FiscHER-ScHLEMM, W. E., and MOSER, E. 1958. [TRIALS WITH AN AUGER-TYPE PLOW.] Landtechnische Forsch. (Munich) 8: 95-101, illus. (119) FISHER, R. A. 1926. ON THE CAPILLARY FORCES IN AN IDEAL SOIL, CORRECTION OF FORMULA GIVEN BY w. B. HAINES. Jour. Agr. Sci. 16: 492- 505, illus. (120) 1928. FURTHER NOTE ON THE CAPILLARY FORCES IN AN IDEAL SOIL. Jour. Agr. Sei. 18: 406-410, illus. (121) FLEHR, F. 1953. [POSSIBILITIES OF A MORE STREAMLINED DESIGN OF AGRICUL- TURAL IMPLEMENTS AND TOOLS.] Laudtechnische Forsch, (Munich) 3: 53-56. (122) FLYNN, P. F., and STRAIT, J. 1962. AN ANALYSIS OF SOIL FORCES ACTING ON THE ROTARY HOE. Amer. Soc. Agr. Engin. Paper 62-145, 7 pp., illus. (123) FORREST, P. J. 1958. TRANSPORT. Tillage and Traction Equipment Seminar Proc. U.S. Dept. Agr., Agr. Res. Serv., ARS-42-16, 54 pp., illus. (124) REED, I. F., and CONSTANTAKIS, G. V. 1962. TRACTIVE CHARACTERISTICS OF RADIAL PLY TIRES. AmCr. SoC. Agr. Engin. Trans. 5: 108, 115. illus. (125) FOSTER, C. R. KNIGHT, S. J. and RULA, A. A. 1958. SOIL TRAFFiCABiLiTY. In Tillage and Traction Equipment Seminar Proc, U.S. Dept. Agr., Agr. Res. Serv., ARS 42-16, pp. 35-43, illus. (126) FOUNTAINE, E. R. 1953. A SOIL ADHESION METER. Nati. lust. Agr. Engin. Tech. Memo. 96, 9 pp., illus. (127) 1954. INVESTIGATIONS INTO THE MECHANISM OF SOIL ADHESION. Jour. Soil Sei. 5: 251-263, illus. (128) Brown, N. J., and Payne, P. C. J. 1956. THE MEASUREMENT OF SOIL WORKABILITY. 6th lutematl. Cong. Soil. Sei.' (Paris) 6: 495-504, illus. (129) and PAYNE, P. C. J. 1951. THE SHEAR STRENGTH OF TOP SOILS. Nati. lUSt. Agr. Eugiu. Tech. Memo. 42, 7 pp., illus. (130) and PAYNE, P. C. J. 1952. THE EFFECT OF TRACTORS ON VOLUME WEIGHT AND OTHER SOIL PROPERTIES. Nati. Inst. Agr. Engin. CS 17, 34 pp., illus. (131) and PAYNE, P. C. J. 1954. CAUSES OF NON-SCOURING IN SOIL WORKING IMPLEMENTS. Fifth Internatl. Cong. Soil Sei. Trans. (Leopoldville) 2: 35-45, illus. (132) Fouss, J. L., and DONNAN, W. W. 1962. PLASTIC-LINED MOLE DRAINS. Agr. Engin. 43: 512-515, illus. (133) Fox, W. R., and BOCKHOP, C. W. 1962. CHARACTERISTICS OF A TEFLON-COVERED SIMPLE TILLAGE TOOL. Amer. Soe. Agr. Engin. Paper 62-649, 10 pp., illus. (134) FREITAG, D. R. 1962. THE PERFORMANCE OF TRANSPORT WHEELS IN SAND. Aubum Univ. AN 604 Spec. Prob. Rpt., 29 pp., illus. (135) FREVERT, R. K. 1940. MECHANICS OF TILLAGE. M. S. Thesis. Iowa State Univ., Ames, illus. (136) FROELICH, O. K. 1934. [PRESSURE DISTRIBUTION IN FOUNDATION SOILS.] Waterways Expt. Sta. Vieksburg, Miss. [Eng. Translation 46-11], illus. (137) GANTT, C. W. Jr. 1962. PENETRATING ABILITIES AND POWER REQUIREMENTS OF DISK COULTERS. M.S. Thesis, Univ. of Georgia, 47 pp., illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 467

(138) GARBOTZ, G., and DREES, G. 1958. [EXPERIMENTS ON THE PLAY OF FORCES WITH FLAT EXCAVATOR CUTTING TOOLS. MEDIUM SAND AND SLIGHTLY BINDING SANDY SILT WITH SPECIAL CONSIDERATION OF THE LEVELING BLADES AND PLANE SCRAPER BUCKET CUTTING EDGES.] RcS. Rpt. 430, illus. Min. of Trade and Com., North-Rhine Westphalia, West Germany. [Engin. Res. Devlpmt. Lab., Ft. Belvoir, Va., Eng. Translation T-318.] (139) GARDNER, W. R. 1956. REPRESENTATION OF SOIL AGGREGATE-SIZE DISTRIBUTION BY A LOGARITHMIC-NORMAL DISTRIBUTION. Soil Sci. SOC. Amer. Proc. 20: 151-153, illus. (140) GAVRILOV, F. L, and KORUSCHKIN, E. N. 1954 [THE UNDERSIDE CHAMFER OF PLOUGH SHARES.] SelkhOZma- shina 3 : 18-21, illus. [Nati. Inst. Agr. Engin., Eng. Trans- lation. 21.] (141) GEIGER, M. L. 1961. VALUE OF DIFFERENTIAL LOCKS FOR FARM TRACTORS. Agr. Engin. 42: 124-127, 139, 140, illus. (142) GETZLAFF, G. 1953. [THE FORCES ACTING DURING THE PLOWING OF STONY GROUND.] Grundlagen der Landtechnik 5: 7-15, illus. [Nati. Inst. Agr. Engin., Eng. Translation 5.] (143) 1953. [COMPARATIVE STUDIES ON THE FORCES ACTING ON STANDARD PLOUGH BODIES.] Grundlagen der Landtechnik 5: 16-35, illus. [Nati. Inst. Agr. Engin., Eng. Translation 6.] (144) 1953. [THE FORCES ACTING ON POWER DRIVEN PLOUGH DISCS.] Grund- lagen der Landtechnik 5: 36-41, illus. [Nati. Inst. Agr. Engin., Eng. Translation 7.] (145) and SOEHNE, W. 1959. [FORCES AND POWER REQUIREMENTS OF FREELY ROTATING AND DRIVEN PLOUGH DISCS ON HARD, DRY, CLAYEY LOAM.] Grund- lagen der Landtechnik 11: 40-52, illus. [Nati. Inst. Agr. Engin., Eng. Translation 106.] (146) GiLL, W. R. 1959 THE EFFECTS OF DRYING ON THE MECHANICAL STRENGTH OF LLOYD CLAY. Soil Sci. Soc. Amcr. Proc 23: 255-257, illus.

1959. SOIL COMPACTION BY TRAFFIC. Agr. Eugiu. 40: 392-394, 400, 402, illus. (148) 1961. MECHANICAL IMPEDANCE OF PLANTS BY COMPACT SOILS. Amer. Soc. Agr. Engin. Trans. 4: 238-242, illus. (149) and MCCREERY, W. F. 1960. RELATION OF SIZE OF CUT TO TILLAGE TOOL EFFICIENCY. Agr. Engin. 41: 372-374, 381, illus. (150) and REAVES, C. A. 1956. COMPACTION PATTERNS OF SMOOTH RUBBER TIRES. Agr. Eugiu. 37: 677-680, 684, illus. (151) and REAVES, C. A. 1957. RELATIONSHIPS OF ATTERBERG LIMITS AND CATION-EXCHANGE CAPACITY TO SOME PHYSICAL PROPERTIES OF SOIL. Soil Sci. Soc. Amer. Proc. 21: 491^94, illus. (152) GiLMOUR, W. D. 1960. AN ELECTRONIC POTATO SCREENER. Jour. Agr. Eugiu. Res. 5: 437-440, illus. (153) GLASSTONE, S. 1946. TEXTBOOK ON PHYSICAL CHEMISTRY. Ed. 2, 1320 pp., illUS. New York. (154) GLERUM, J. C. 1954. [CAGE WHEELS.] Landb. Meeh. (Wageningen, Netherlands) 5: 18. 468 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

(155) GLIEMEROTH, G. 1953. [INVESTIGATIONS OF COMPACTION AND DISPLACEMENT PHE- NOMENA IN THE SOIL UNDER WHEEL AND TRACK VEHICLES.] ,,^^ Ztschr. f. Acker und Pflanzenbau 96: 218-234, illus. (156) GoHLicH, H. 1955. [INVESTIGATIONS ON A POWER DRIVEN TRAILER.] Landtechnik 10(6) : 127, illus. [Nati. Inst. Agr. Engin., Eng. Translation

(157) GOLDBECK, A. T. 1916. AN APPARATUS FOR DETERMINING SOIL PRESSURES AuiCr SOC ,,^^, ^ Testing Mater. Proc. 16: 310-319, illus. (158) GORYACHKIN, V. P. 1940. COLLECTED WORKS, Sel'khozgiz, Moscow. (159) GORDON, E. D. 1941. PHYSICAL REACTIONS OF SOIL ON PLOW DISKS AsT Euffin 22: 205-208, illus. * ^ * (160) GOULD, J. S., and WATERMAN, H. 1867. REPORT ON TRIALS OF PLOWS. N. Y. State Soc. Trans 27« 385-656, illus. (161) GREACEN, E. L. 1959. THE STRENGTH OF CULTIVATED SOIL. Jour. Agr. Engin. Res. 4: 60-61, illus. (162) 1960. AGGREGATE STRENGTH AND SOIL CONSISTENCE. 7th Interna tl Cong. Soil Sei. Trans. (Madison, Wis.) 1: 256-264 illus (163) ■ 1960. WATER CONTENT AND SOIL STRENGTH. Jour. Soil Soi 11' 313-333. Illus. (164) GREEN, H. C. 1957. SOME EXPERIMENTS ON THE CLEANING OF SUGAR BEETS. Jour Agr. Engin. Res. 2: 209-216, illus. (165) GREEN WALD, D. U. 1957. LINEAR PROGRAMMING. 75 pp., illus., New York (166) GROSSMAN, R. B., and CLINE, M. G. 1957. FRAGIPAN HORIZONS IN NEW YORK SOILS : II. RELATIONSHIPS BETWEEN RIGIDITY AND PARTICLE SIZE DISTRIBUTION Soil Sci Soc. Amer. Proc. 21: 322-325, illus. (167) GuNN, J. T., and TRAMONTINI, V. N. 1955. OSCILLATION OF TILLAGE IMPLEMENTS. Agr. Engin. 36:725-

(168) HAEFELI, R. 1951. INVESTIGATIONS AND MEASUREMENTS OF THE SHEAR STRENGTH OF SATURATED COHESIVE SOILS. Geotechnioue 2: 186-208 illus. ' (169) HAINES, W. B. 1925. STUDIES IN THE PHYSICAL PROPERTIES OF SOILS. I. MECHANICAL PROPERTIES CONCERNED IN CULTIVATION. Jour Affr Soi 1^' 178-200, illus. • ^ (170) HALL, A. D. 1962. A METHODOLOGY FOR SYSTEMS ENGINEERING 478 DD illn«î Princeton, N. J. ^^*' ' (171) HANAVAN, M. T., and REECE, A. R. 1961. IMPACT LOADS ON TRACTOR IMPLEMENTS. Jour Aer En^in Res. 6: 161-168, illus. ' ^ (172) HANKS, R. J., and HARKNESS, K. A. 1956. SOIL PENETROMETER EMPLOYS STRAIN GAGES. Agr Euirin 37: 553-554, illus. ^ J^n^m. (173) HARDY, E. A. 1938. TILLAGE IN RELATION TO WEED ROOT SYSTEMS. Agr. Engin 19: 435-438, illus. (174) HARDY, F. 1925. COHESION IN COLLOIDAL SOILS. Jour. Agr. Sei. 15: 420-433, SOIL DYNAMICS IN TILLAGE AND TRACTION 469

(175) HARRIS, W. L., BUCHELE, W. F., and MALVERN, L. E. 1964. RELATIONSHIP OF MEAN STRESS, VOLUMETRIC STRAIN AND DY- NAMIC LOADS IN SOIL. Amei*. Soc. Agr. Engin. Trans. 7: 362-364, 369, illus. (176) HARRISON, W. L., JR. 1961. ANALYTICAL PREDICTION OF PERFORMANCE FOR FULL SIZE AND SMALL SCALE MODEL VEHICLES. Ist IntematL Gonf. Mech. Soil-Vehicle Systems Proc. (Turin), pp. 678-702, illus. (177) HARROUND, D. 1953. INVESTIGATION OF FURTHER USEFULNESS MARK. II. SOIL TRUSS. Contract Rpt. N. O. Y. 73519, Jour. Civ. Engin. Dept, Univ. of Pa., 72 pp., illus. (178) HAGEDUS, E. 1962. PRESSURE DISTRIBUTION UNDER RIGID WHEELS. Amer. SoC. Agr. Engin. Paper 62-647, 13 pp., illus. (179) HEITSHU, D. C. 1952. THE KINEMATICS OF TRACTOR HITCHES. Agr. Eugiu. 33: 343- 346, 356, illus. (180) HENDRICK, J. C, and BUCHELE, W. F. 1963. THE TILLAGE ENERGY OF A VIBRATING TILLAGE TOOL. Amcr. Soc. Agr. Engin. Trans. 6: 213-216, illus. (181) and VANDEN BERG, G. E. 1961. STRENGTH AND ENERGY RELATIONS OF A DYNAMICALLY LOADED CLAY SOIL. Amer. Soc. Agr. Engin. Trans. 4: 31-32, 36, illus. (182) HILL, R. 1950. THE MATHEMATICAL THEORY OF PLASTICITY. 373 pp., illus. Oxford. (183) HoLBERT, J. R., and KOEHLER, B. 1924. ANCHORAGE AND EXTENT OF CORN ROOT SYSTEMS. Jour. Agr. Res. 27: 71-73, illus. (184) HOUGH, B. K. 1957. BASIC SOILS ENGINEERING. 513 pp., illus. Ncw York. (185) HOVÁNESIAN, J. D. 1958. DEVELOPMENT AND USE OF A VOLUMETRIC TRANSDUCER FOR STUDIES OF PARAMETERS UPON SOIL COMPACTION. Ph. D. Thesis, Mich. State Univ., 77 pp., illus. (186) and BUCHELE, W. F. 1959. DEVELOPMENT OF A RECORDING VOLUMETRIC TRANSDUCER FOR STUDYING EFFECTS OF SOIL PARAMETERS ON COMPACTION. Amer. Soc. Agr. Engin. Trans. 2: 78-81, illus. (187) HUECKEL, S. 1957. MODEL TESTS ON ANCHORING CAPACITY OF VERTICAL AND IN- CLINED PLATES. 4th Internatl. Conf. Soil Mech. and Found. Engin. Proc. (London) 11: 203-206, illus. (188) HuLBURT, W. C, and MENZEL, R. G. 1953. SOIL MIXING CHARACTERISTICS OF TILLAGE IMPLEMENTS. Agr. Engin. 34: 702-704, 706, 708, illus. (189) HuLST, H., GoHLicH, H., and SOCHTING, B. 1957. [INVESTIGATIONS ON LIFTING SHARES FOR SUGAR BEETS.] Zucker 10: 535-538, illus. [Nati. Inst. Agr. Engin., Eng. Translation 47.] (190) JAEGER, J. C. 1956. ELASTICITY, FRACTURE AND FLOW WITH ENGINEERING AND GEO- LOGICAL APPLICATIONS. 152 pp., illus. New York. (191) JAMISON, V. C. 1945. THE PENETRATION OF IRRIGATION AND RAIN WATER INTO SANDY SOILS OF CENTRAL FLORIDA. Soil Sci. Soc. Amer. Proc 10: 25- 29, illus. (192) and REED, I. F. 1949. DURABLE ASBESTOS TENSION TABLES. Soil Sei. 67: 311-318, illus. (193) 1954. THE EFFECT OF SOIL CONDITIONERS ON FRIABILITY AND COM- PACTiBiLiTY OF SOILS. Soil Sci. Soc. Amer. Proc 18: 391- 394, illus. 470 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE (194) 1960. WATER MOVEMENT RESTRICTION BY PLANT RESIDUES IN A SILT LOAM SOIL. 7th Internat!. Soil Sei. Trans. (Madison, Wis.) 1: 464-472, illus. (195) and WEAVER, H. A. 1952. THE RELATIONSHIP OF MOISTURE AND MICROPOROSITY TO THE HARDNESS OF LLOYD CLAY. AgTon. Jour. 44: 337, illus. (196) WEAVER, H. A., and REED, I. F. 1951. THE DISTRIBUTION OF TRACTOR TIRE COMPACTION EFFECTS IN CECIL CLAY. Soil Sci. Soc. Amer. Proc. 15: 34-37, illus. (197) JANERT, H. 1955. [THE GRIEFWALDER PIPE-LAYING MACHINE AND ITS OPERATION.] Wasserwirtschaft-Wassertechnik 5: 123-150, illus. [U.S. Dept. Agr., Agr. Res. Serv., Soil and Water Conserv. Res. Div,. Eng. Translation Spec. Rpt. 79.] (198) JANOSI, Z. 1962. THEORETICAL ANALYSIS OF THE PERFORMANCE OF TRACKS AND WHEELS OPERATING ON DEFORMARLE SOIL. Amer. SoC. Agr. Engin. Trans. 5: 133-134, 146, illus. (199) JEFFERSON, T. 1799. DESCRIPTION OF A MOULDBOARD. London Phil. Soc. Proc, pp 313-322, illus. (200) JENKIN, C. F. 1931. THE PRESSURE EXERTED BY GRANULAR MATERIAL: AN APPLICA- TION OF THE PRINCIPLES OF DILANTANCY. Roy. Soc. LoudOU, Proc, Ser. A, 131: 53-89, illus. (201) 1932. LETTER TO THE EDITOR. Engineering 134: 151. (202) JOHNSON, O. E. 1960. DESIGN FACTORS IN A SPRING-TRIP BEAM ASSEMBLY FOR MOLD- BOARD PLOWS. Amer. Soc Agr. Engin. Trans. 3: 2: 61-62, illus. (203) JOHNSON, W. H. PERSONAL COMMUNICATION. Agr. Engin. Dept., Ohio State Univ. (204) KABURAKI, H., and Kisu, M. 1959. [STUDIES ON CUTTING CHARACTERISTICS OF PLOWS.] KantO- Tosan Agr. Exp. Sta. Jour. (Konosu, Japan) 12: 90-114, illus. [Nati. Inst. Agr. Engin., Eng. Translation 79.] (205) and Kisu, M. 1960. [STUDIES ON CUTTING CHARACTERISTICS OF PLOUGHS. PART II. SOIL STICKING TO THE PLOUGH.] Kauto-Tosau Agr. Expt. Sta. Journ. (Konosu, Japan) 16: 309-322, illus. [Nati. Inst. Agr. Engin., Eng. Translation 108.] (206) KARATISH, A. 1955. [THE WEAR OF THE WORKING ELEMENTS OF SOIL CULTIVATION IMPLEMENTS.] Mashiuo-traktomdia Sta. 15: 30-32, illus. [Nati. Inst. Agr. Engin., Eng. Translation 29.] (207) KAWAMURA, N. 1952. [STUDY OF THE PLOW SHAPE. (1). APPROXIMATE ANALYSIS OF THE SOD PLOW.] Soc Agr. Mach. Jour. (Japan) 13: 1-3, illus. (208) 1952. [STUDY OF THE PLOW SHAPE. (2). ANALYSIS OF THE SOD PLOW CONSIDERING STRENGTH OF SOIL.] Soc Agr. Mach Jour (Japan) 13: 4-8, illus. (209) 1952. [STUDY OF THE PLOW SHAPE. (3). STUDY ON SOIL CUTTING AND PULVERIZATION (1).] Soc Agp. Mach. Jour. (Japan) 14 (3) : 65-71, illus. (210) 1953. [STUDY OF THE PLOW SHAPE. (4.) STUDY ON SOIL CUTTING AND PULVERIZATION (2.)] Soc Agr. Mach. Jour. (Japan) 15(3) : 90-94, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 471

(211) 1957. [CHARACTERISTICS OF SOIL RESISTANCE OF VARIOUS SHAPE MOLDBOARD PLOWS.] Osaka [Japan] Univ. Bui. Ser. B 7: 65-75, illus. (212) 1957. [EXPERIMENTAL STUDIES OF PLOW SHAPES.] SOC. Agr. Mach. Jour., (Japan) 19: 97-100, illus. (213) 1958. DYNAMIC BEHAVIOR OF SOIL. II. HIGH SPEED TRIAXIAL COM- PRESSION TEST. Soc. Agr. Mach. Jour. (Japan) 20: 101- 103, illus. (214) KEEN, B. A. 1931. THE PHYSICAL PROPERTIES OF THE SOIL. 380 pp., lUUS. NCW York. (215) and HAINES, W. B. 1925. STUDIES IN SOIL CULTIVATION. Jour. Agr. Sei. 15: 375-406, illus. (216) KERESELIDZE, S. Y., KHUKHUNI, T. V., and SHKOLNIK, E. B. 1959. [INVESTIGATIONS INTO THE OPERATION OF THE AUTOMATIC STABILIZER OF THE USG-12A HILLSIDE TRACTOR.] TraktOry Í Sel'khozmashiny (Moscow) 3: 4, illus. [Jour. Agr. Engin. Res. 4: 267-273, Eng. Translation.] (217) KHAMIDOV, A. 1961. [USE OF GAMMA-RAYS IN THE STUDY OF THE EFFECTS OF WHEELS ON THE SOIL.] Trudy VIM 28: 94-107, illus. [Jour. Agr. Engin. Res. 6: 147-152, Eng. Translation.] (218) KiRKHAM, D., DEBOODT, M. F., and DELEENHEER, L. 1959. MODULUS OF RUPTURE DETERMINATION ON UNDISTURBED SOIL CORE SAMPLES. Soil Scl. 87: 141-144, illus. (219) KLIEFOTH, F. 1954. [STRUCTURE DAMAGE THROUGH THE SLIDING OF WHEELS.] Landtechnik 9: 122-123, illus. (220) KNIGHT, S. J. and FREITAG, D. R. 1962. MEASUREMENT OF SOIL TRAFFICABILITY CHARACTERISTICS. Amer. Soc. Agr. Engin. Trans., 5: 121-124, 132, illus. (221) KNOX, E. G. 1957. FRAGIPAN HORIZONS IN NEW YORK SOILS. III. THE BASIS OF RIGIDITY. Soil Sci. Soc. Amer. Proc. 21: 326-330, illus. (222) KOLCHIN, N. N. 1957. [COMBINED PNEUMATIC AND MECHANICAL SEPARATION OF POTATO TUBERS FROM CLODS.] Sel'khozmashina 3 : 19-21, illus. [Jour. Agr. ^ngin. Res. 2: 238-240, Eng. Translation.] (223) KONDNER, R. L. 1958. A NON-DIMENSIONAL APPROACH TO THE VIBRATORY CUTTING, COMPACTION AND PENETRATION OF SOILS. Tech. Rpt. 8 by the Johns Hopkins Univ. to U.S. Army Corps of Engin., Water- ways Expt. Sta., Vicksburg, Miss., 183 pp., illus. (224) 1959. THE VIBRATORY CUTTING, COMPACTION AND PENETRATION OF SOILS. Tech. Rpt. 7 (Part II), by the Johns Hopkins Univ. to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss., 51 pp., illus. (225) 1962. A PENETROMETER STUDY OF THE IN SITU STRENGTH OF CLAYS. Mater. Res. and Standards 2: 193-195, illus. (226) and AYRE, R. S. 1959. STUDY OF VIBRATORY CUTTING, PENETRATION AND COMPACTION OF SOILS. Tech. Rpt. 6 by the Johns Hopkins Univ. to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss., 7 pp., illus. (227) AYRE, R. S., and CHAE, Y. S. 1958. LABORATORY INVESTIGATION OF THE VIBRATORY CUTTING AND PENETRATION OF SOILS (part 1). Tcch. Rpt. 5 by the Johns Hopkins Univ. to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss., 12 pp., illus. 472 AGRICULTURE HANDBOOK 816, U.S. DEPT. OF AGRICULTURE

(228) KOOPMAN, N. P. 1957. [RESEARCH ABOUT THE WEAR OF PLOW SHARES.] Rpt. Agr. State Univ., Dept. Agr. Engin., Wageningen, Netherlands, illus. (229) KORAYEM, A. Y. 1961. FRicTiONAL PROPERTIES OF ARTIFICIAL SOILS. Unpublished M. S. Thesis, Univ. of Calif., illus. (230) KosTRiTSYN, A. K. 1956. [CUTTING OF A COHESIVE MEDIUM WITH KNIVES AND CONES.] Vsesoiuzz. Akad. Sel'skokhoziaistvennykh Nauk. Zeml. Mekh. Shorn. Trudov. (Leningrad) 3: 247-290, illus. [Nati. Inst. Agr. Engin., Eng. Translation 58.] (231) KRUTIKOV, N. P., SMIRNOV, I. I., STSCHERBAKOV, K. F., and POPOV, I. F. 1955. THEORY, CALCULATION AND DESIGN OF FARM MACHINERY. V, I. MACHINERY FOR SOIL CULTIVITION, SOWING, AND PLANT CUL- TIVATION. 690 pp., illus. Berlin. (232) KUHN, G. 1954. [SHAPE OF BULLDOZER BLADES TO ATTAIN THE SMALLEST FILLING RESISTANCE.] Ver. Deut. Ingen. Ztschr. 96: 373-377, illus. (233) 1954. [SHAPE OF BULLDOZER BLADES TO ATTAIN THE SMALLEST FILLING RESISTANCE.] Ver. Deut. Ingen. Ztschr. 96: 982-986, illus. (234) KUMMER, F. A. 1939. THE DYNAMIC PROPERTIES OF SOIL. VIII. THE EFFECT OF CERTAIN EXPERIMENTAL PLOW SHAPES AND MATERIALS ON SCOURING IN HEAVY CLAY SOILS. Agr. Eugiu. 20: 111-114, illus. (235) and NICHOLS, M. L. 1938. THE DYNAMIC PROPERTIES OF SOIL, VII. A STUDY OF THE NATURE OF PHYSICAL FORCES GOVERNING THE ADHESION BE- TWEEN SOIL AND METAL SURFACES. Agr. Eugiu. 19: 73-78, illus. (236) KYNAZEV, A. A. 1957. [DRAUGHT RESISTANCE OF CHISEL PLOUGHS.] Sel'khozmashina 2: 7-9, illus. (Nati. Inst. Agr. Engin., Eng. Transla- tion 89.) (237) LAL, R. 1959. MEASUREMENT OF FORCES ON MOUNTED IMPLEMENTS. Amer Soc. Agr. Engin. Trans. 2: 109-111, illus. (238) LAMBE, T. W. 1951. SOIL TESTING FOR ENGINEERS. 165 pp., illus. New York (239) LAMBE, T. W. 1958. THE STRUCTURE OF COMPACTED CLAY. Ainer. Soc. Civ. Engin Proc. 84 : Paper 1654, 34 pp., illus. (240) 1958. THE ENGINEERING BEHAVIOR OF COMPACTED CLAY. Amer. SoC. Civ. Engin. Proc. 84 : Paper 1655, 34 pp., illus. (241) LAND LOCOMOTION LABORATORY, DETROIT ARSENAL, WARREN, MICH. 1956. PRELIMINARY STUDY OF SNOW VALUES RELATED TO ' VEHICLE PERFORMANCE. Tech. Memo M02, 27 pp., illus. (242) 1957. AN INVESTIGATION OF GUN ANCHORING SPADES UNDER THE AC- TION OF IMPACT LOADS. Rpt. 19, 33 pp., illus. (243) 1957. ARTIFICIAL SOILS FOR LABORATORY STUDIES IN LAND LOCOMOTION Rpt. 20, 29 pp., illus. (244) 1957. STUDY OF SNOW VALUES RELATED TO VEHICLE PERFORMANCE Rpt. 23, 31 pp., illus. (245) 1958. A SOIL VALUE SYSTEM FOR LAND LOCOMOTION MECHANICS ReS Rpt. 5, 94 pp., illus. (246) 1960. EVALUATION OF CONDUAL TIRE MODEL. Rpt. 60, 28 pp., illuS. SOIL DYNAMICS IN TILLAGE AND TRACTION 473

(247) 1960. THE MECHANICS OF WALKING VEHICLES. Rpt. 71, 67 pp., illus. (248) 1961. BEVAMETER 100. A NEW TYPE OF FIELD APPARATUS FOR MEAS- URING LOCOMOTIVE STRESS-STRAIN RELATIONSHIPS IN SOILS. 1st Internatl. Conf. Mech. Soil-Vehicle Systems Proc, (Tu- rin), pp. 331-361, illus. (249) 1961. THE ANALYTICAL DETERMINATION OF DRAWBAR PULL AS A FUNCTION OF SLIP FOR TRACKED VEHICLES IN DEFORMARLE SOILS. 1st Internatl. Conf. Mech. Soil-Vehicle Systems, Proc. (Tu- rin), pp. 707-736, illus. (250) LANGE, H. 1957. [ABILITY OF PNEUMATIC TIRES TO ABSORB THE LATERAL FORCES ACTING ON AGRICULTURAL MACHINES WHEN TRAVELING ACROSS THE SLOPE.] Grundlagen der Landtechnik 9: 109-112, illus. (251) LASZLO, K. 1951. [EFFECT OF TILLAGE MACHINES ON SOIL STRUCTURE.] Expt. Inst. for Agr. Mach. ybk. (Budapest) v. II, p. 175-208, illus. (252) LECHNER, F. G. and MCCOLLY, H. F. 1959. ABRASIVE-WEAR RESISTANCE OF HARD-FACING MATERIALS USED ON AGRICULTURAL TILLAGE TOOLS. Amcr. SOC. Agr. EugiU. Trans. 2: 55-57, illus. (253) LEWIS, W. A. 1954. FURTHER STUDIES IN THE COMPACTION OF SOIL AND THE PER- FORMANCE OF COMPACTION PLANT. [Gt. Brit.] Dept. Sei. and Indus. Res. Road Res. Lab., Tech. Paper 33, illus. (254) 1957. A STUDY OF SOME OF THE FACTORS LIKELY TO AFFECT THE PERFORMANCE OF IMPACT COMPACTORS ON SOIL. 4th Internatl. Conf. Soil Mech. and Found. Engin. Proc. (London) 2: 145- 150, illus. (255) LoRENZEN, C, JR. 1950. THE DEVELOPMENT OF A MECHANICAL ONION HARVESTER. Agr. Engin. 31: 13-15, illus. (256) LOVE, A. E. H. 1929. THE STRESS PRODUCED IN A SEMI-INFINITE BODY BY PRESSURE ON PART OF THE BOUNDARY. Roy. Soc. Loudon, Phil. Trans., Ser. A, 228: 277^20. (257) LULL, H. W. 1959. SOIL COMPACTION ON FOREST AND RANGE LANDS. U.S. Dept. Agr. Misc. Pub. 768, 33 pp., illus. (258) LUTZ, J. F. 1947. APPARATUS FOR COLLECTING UNDISTURBED SOIL SAMPLES. SOIL Sei. 64: 399-401, illus. (259) LYSAGHT, V. E. 1947. THE KNOOP INDENTER AS APPLIED TO TESTING NON-METALLIC MATERIALS RANGING FROM PLASTICS TO DIAMONDS. Amer. SoC. Testing Mater. Bui. 138, 39 pp., illus. (260) MACLEAN, D. J., and ROLFE, D. W. 1946. A LABORATORY INVESTIGATION OF ELECTRO-OSMOSIS IN SOILS. Philos. Mag. 37 : 863-873, illus. (261) MCCLELLAND, J. H. 1956. INSTRUMENT FOR MEASURING SOIL CONDITION. Agr. Engin. 37: 480-481, illus. (262) MCCREERY, W. F. 1959. EFFECT OF DESIGN FACTORS OF DISKS ON SOIL REACTIONS. AMCR. Soc. Agr. Engin. Paper 59-622, 6 pp., illus. (263) and NICHOLS, M. L. 1956. THE GEOMETRY OF DISKS AND SOIL RELATIONSHIPS. Agr. Eugiu. 37: 808-812, 820, illus. (264) MCFARLANE, J. S., and TABOR, D. 1950. ADHESION OF SOLIDS AND THE EFFECT OF SURFACE FILMS. Roy. Soc. London, Proc, S©r. A, 202: 224-243, illus. 474 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

(265) and TABOR, D. 1950. RELATION BETWEEN FRICTION AND ADHESION. Roy. SOC. Lon- don, Proc, Ser. A, 202: 244-253, illus. (266) McKiBBEN, E. G. 1926. THE SOIL DYNAMICS PROBLEM. Agr. Engin. 7: 412-413, illus. (267) 1938. SOME KINEMATIC AND DYNAMIC STUDIES OF RIGID TRANSPORT WHEELS FOR AGRICULTURAL EQUIPMENT. lOWa Agr. Expt. Sta. Res. Bui. 231, pp. 321-390, illus. (268) 1959. ENGINEERING IN AGRICULTURE. Agr. Engin. 40: 385, 412, 414, illus. (269) and BERRY, M. O. 1952. THE VALUE OF REPLICATIONS IN RESEARCH. Agr. Eugiu. 33: 792, 798, illus. (270) and DAVIDSON, J. B. 1939. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. II. ROLL- ING RESISTANCE OF INDIVIDUAL WHEELS. Agr. Engin. 20* 469-473, illus. (271) and DAVIDSON, J. B. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. III. EFFECT OP INFLATION PRESSURE ON THE ROLLING RESISTANCE OF PNEU- MATIC IMPLEMENT TIRES. Agr. Engin. 21: 25-26, illus. (272) and DAVIDSON, J. B. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. IV. EFFECT OF OUTSIDE AND CROSS-SECTIONAL DIAMETERS ON THE ROLLING RESISTAT^CE OP PNEUMATIC IMPLEMENT TIRES. Agr. Eugiu. 21 : 57-58, illus. (273) and DAVIDSON, J. B. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINERY. V. EFFECT OF WHEEL ARRANGEMENT ON ROLLING RESISTANCE. Agr. Euffin. 21: 95-96, illus. (274) and DAVIDSON, J. B. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. VI. EF- FECTS OF STEEL WHEEL RIM SHAPE AND PNEUMATIC TIRE- TREAD DESIGN ON ROLLING RESISTANCE. Agr. Engin. 21 : 139- 140, illus. (275) and DAVIDSON, J. B. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. IX. EFFEC- TIVE RADIUS AND SLIPPAGE. Agr. Eugiu. 21: 275-276. illus (276) and GREEN, R. L. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINERY. VII. RELATIVE EFFECTS OF STEEL WHEELS AND PNEUMATIC TIRES ON AGRICULTURAL SOILS. Agr. Engin. 21: 183-185, illus. (277) and HULL, D. O. 1940. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. VIII. SOIL PENETRATION TESTS AS A MEANS OF PREDICTING ROLLING RE- SISTANCE. Agr. Engin. 21: 231-234, illus. (278) and REED, I. F. 1952. THE INFLUENCE OF SPEED ON THE PERFORMANCE CHARACTER- ISTICS OF IMPLEMENTS. Paper, SAE Nati. Tractor Mtg. Milwaukee, Wis., 5 pp., illus. ' (279) and THOMPSON, H. J. 1939. TRANSPORT WHEELS FOR AGRICULTURAL MACHINES. I. COM- PARATIVE PERFORMANCE OF STEEL WHEELS AND PNEUMATIC TIRES ON TWO MANURE SPREADERS OF THE SAME MODEL. AsT Engin. 20: 419^22, illus. * (280) McMuRDiE, J. L. 1963. SOME CHARACTERISTICS OF THE SOIL DEFORMATION PROCESS ,^^_ Soil Sei. Soc. Amer. Proc. 27: 251-254, illus. (281) and DAY, P. R. 1958. COMPRESSION OF SOIL BY ISOTROPIC STRESS. Soil Sci SoC Amer. Proc. 22: 18-21, illus. (282) and DAY, P. R. 1960. SLOW TESTS UNDER SOIL MOISTURE SUCTION. Soil Sci Soc Amer. Proc. 24: 441-444, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 475

(283) MCRAE, J. L. 1950. A STUDY OF STRESSES IN SOIL DURING LABORATORY COMPACTION. [Unpublished.] Dept. of Civil Engin., Northwestern Univ., 14 pp., illus. (284) MAACK, O. 1957. [THE MECHANICAL SEPARATION OF POTATOES AND STONES.] Landtechnische. (Munich) Forsch. 7: 71-78, illus. [Nati. Inst. Agr. Engin., Eng. Translation 35.] (285) 1957. [THE SEPARATION OF POTATOES AND STONES ON THE BASIS OF RESILIENCE AND ROLLING RESISTANCE,] Landtcchnishc. Forsch. (Munich) 7: 106-110, illus. [Nati. Inst. Agr. Engin., Eng. Translation 36.] (286) MACKSON, C. J. 1962. THE EFFECT OF ELECTRO-OSMOSIS ON SOIL TO STEEL SLIDING FRICTION AS INFLUENCED BY SPEED, VOLTAGE AND SOIL MOIS- TURE. Amer. Soc. Agr. Engin. Paper 62-650, 8 pp., illus. (287) MANLEY, P. L. 1960. AN INVESTIGATION OF MECHANICAL AND PHYSICAL FACTORS INFLUENCING THE STABILITY OF MOLE DRAINS UNDER LOAD. M. S. Thesis, Cornell Univ., illus. (288) 1960. PLASTIC DRAIN LINERS EVALUATED BY PNEUMATIC TEST CHAM- BER. Agr. Engin. 41: 824, illus. (289) MARSHAK, A. L. 1956. [SURFACE SHAPE OF PNEUMATIC TIRES IN CONTACT WITH THE SOIL.] Sel'khozmashina 3: 22-24, illus. [Off. Tech. Serv., Translation 60-21084.] (290) 1957. [ROLLING RESISTANCE OF PNEUMATIC TIRES ON FARM MACHINES.] Sel'khozmashina 1: 13-16, illus. (291) MARSHALL, T. J. 1959. RELATIONS BETWEEN WATER AND SOIL. Commonwcalth Bur. Soils (Harpenden, England), Tech. Comm. 50, 91 pp., illus. (292) and QUIRK, J. P. 1950. STABILITY OF STRUCTURAL AGGREGATES OF DRY SOIL. Austral. Jour. Agr. Res. 1: 226-275, illus. (293) MARTINI, Z. 1953. [STUDIES ON SOIL MOVEMENT DURING THE PLOWING OF SLOPES.] Rocz. Nauk Roln. 66-C(2) : 97-123. (294) MAUER, H. C. 1933. A METHOD OF MEASURING THE PRESSURE OF THE SOIL ON PLOWS OR OTHER TILLAGE IMPLEMENTS. M. S. ThesiS, Aubum UuiV., 13 pp., illus. (295) MAYAUSKAS, I. S. 1958. INVESTIGATION OF THE PRESSURE DISTRIBUTION ON THE SURFACE OF A PLOW SHARE IN WORK. Traktory i Sel'khozmashiny 11: 23- illus. [Jour. Agr. Engin. Res. 4: 186-190. 1959, Eng. Translation.] (296) MECH, S. J., and FREE, G. R. 1942. MOVEMENT OF SOIL DURING TILLAGE OPERATIONS. Agr. EugiU. 23: 379-382, illus. (297) MENZEL, R. G., ROBERTS, H., JR., and JAMES, P. E. 1961. REMOVAL OF RADIOACTIVE FALLOUT FROM FARM LAND. PrOg. Rpt. II. Agr. Engin. 42: 69S-699, illus. (298) MEREDITH, H. L. and PATRICK, W. H., JR. 1961. EFFECTS OF SOIL COMPACTION ON SUBSOIL ROOT PENETRATION AND PHYSICAL PROPERTIES OF THREE SOILS IN LOUISIANA. Agron. Jour. 53: 163-167, illus. (299) MILLER, S. A., and MAZURAK, A. P. 1958. RELATIONSHIPS OF PARTICLE AND PORE SIZES TO THE GROWTH OF SUNFLOWERS. Soil Sci. Soc. Amcr. Proc. 22: 275-278, illus. (300) MiscENKO, N. F. 1935. METHODS OF FIXATION AND POROSITY DETERMINATION IN THE STUDY OF SOIL MECHANICS. Agr. Eugiu. 16: 23-29, illus. 476 AGRICULTURE HANDBOOK 316, US. DEPT. OF AGRICULTURE

(301) MITCHELL, N. B. 1961. THE INDIRECT TENSION TEST FOB CONCRETE, MATERIALS, RE- SEARCH, AND STANDARDS. Mater. Res. and Standards 1: 780-788, illus. (302) MOHSENIN, N., WoMOCHEL, H. L., HARVEY, D. J., and CARLETON, W. M. 1956. WEAR TESTS OF PLOWSHARE MATERIALS. Agr. Engin. 37: 816- 820, illus. (303) MÖLLER, R. 1959. DRAFT REQUIREMENTS AND WORKING EFFICIENCY OF RIGID AND SPRING CULTIVATOR TINES. Grundlagen der Landtechnik 11: 85-94, illus. (304) MOORE, P. J. 1961. THE RESPONSE OF SOILS TO DYNAMIC LOADINGS. Tech. Rpt. 7 by the Mass. Inst. Tech., to U.S. Army Corps of Engin., Waterways Expt. Sta., Vicksburg, Miss. 19 pp., illus. (305) MORTON, C. T., and BUCHELE, W. F. 1960. EMERGENCE ENERGY OF PLANT SEEDLINGS. Agr. Engin 41- 428-431, 453-455, illus. (306) MURAYAMA, S., and HATA, S. 1957. ON THE EFFECT OF REMOLDING CLAY. 4th Internatl. Conf. Soil Mech. and Found. Engin. Proc. (London) 1: 80-82, illus. (307) MURNAGHAN, F. D. 1951. FINITE DEFORMATION ON AN ELASTIC SOLID. 140 pp., illUS., New York. (308) MURPHY, G. 1950. SIMILITUDE IN ENGINEERING. 302 pp., New York (309) NAKAYA, U., TADA, M., SEKIDO, Y., and TAKANO, T. 1936. THE PHYSICS OF SKIING. Hokkaido ' Imper. Univ. Faculty Sei. Jour. pp. 265-287, illus. (310) NATIONAL INSTITUTE AGRICULTURAL ENGINEERING, SILSOE, ENGLAND. 1954. SINGLE WHEEL TESTER. Rpt. 40, 23 pp., illus. (311) NATIONAL TILLAGE MACHINERY LABORATORY, AUBURN, ALA. Unpublished Data. (312) NICHOLS, M. L. 1925. THE SLIDING OF METAL OVER SOIL. Agr. Engin. 6: 80-84, illus. (313) 1929. METHODS OF RESEARCH IN SOIL DYNAMICS; AS APPLIED TO IMPLEMENT DESIGN. Ala. Agr. Expt. Sta. Bul. 229, 28 pp illus. (314) 1930. DYNAMIC PROPERTIES OF SOIL AFFECTING IMPLEMENT DESIGN Agr. Engin. 11: 201-204, illus. (315) 1931. THE DYNAMIC PROPERTIES OF SOIL. I., AN EXPLANATION OF THE DYNAMIC PROPERTIES OF SOIL BY MEANS OF COLLOIDAL FILMS. Agr. Engin. 12: 259-264, illus. (316) 1931. THE DYNAMIC PROPERTIES OF SOIL. 11. SOIL AND METAL FRIC- TION. Agr. Engin. 12: 321-324, illus. (317) 1932. THE DYNAMIC PROPERTIES OF SOIL. III. SHEAR VALUES OF UNCEMENTED SOILS. Agr. Engin. 13: 201-204, illus (318) and BAVER, L. D. 1930. AN INTERPRETATION OF THE PHYSICAL PROPERTIES OF SOIL AFFECTING TILLAGE AND IMPLEMENT DESIGN BY MEANS OF ATTERBERG CONSISTENCY CONSTANTS. 2nd Internatl. Cong. Soil Sei. Proc. (Leningrad-Moscow), pp. 175-188, illus (319) and KUMMER, T. H. 1932. THE DYNAMIC PROPERTIES OF SOIL. IV. A METHOD OF ANALY- SIS OF PLOW MOLDBOARD DESIGN BASED UPON DYNAMIC PROPER- TIES OF SOIL. Agr. Engin. 13: 279-285, illus. (320) and RANDOLPH, J. W. 1925. A METHOD OF STUDYING SOIL STRESSES. Agr. EugiU 6' 134- 135, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 477

(321) and REAVES, C. A. 1955 SOIL STRUCTURE AND CONSISTENCY IN TILLAGE IMPLEMENT DE- SIGN. Agr. Engin. 36: 517-520, 522, illus. (322) and REAVES, C. A. . 1958. SOIL REACTION : TO SUBSOILING EQUIPMENT. Agr. Engin. 39 : 340-343, illus. (323) and REED, I. F. 1934. SOIL DYNAMICS, VI. PHYSICAL REACTIONS OF SOILS TO MOLD- BOARD SURFACES. Agr. Engin. 15: 187-190, illus. (324) REED, I. F., and REAVES, C. A. 1958. SOIL REACTION : TO PLOW SHARE DESIGN. Agr. Engin. 39 : 330-339, illus. (325) NIKIFOROFF, C. C. c M d . 1941. MORPHOLOGICAL CLASSIFICATION OF SOIL STRUCTURE. SOll SCl. 52: 193-211, illus. (326) ODELL, R. T., THORNBURN, T. H., and MCKENZIE, L. J. 1960. RELATIONSHIPS OF ATTERBERG LIMITS TO SOME OTHER PROPER- TIES OF ILLINOIS SOILS. Soil Sci. Soc. Amer. Proc. 24: 297- 300, illus. (327) PATTY, R. L., and MINIUM, L. W. 1945. RAMMED EARTH WALLS FOR FARM BUILDINGS. S.D. Agr. Expt. Sta. Bui. 277, 63 pp., illus. (328) PAYNE, P. C. J. 1956. A FIELD METHOD OF MEASURING SOIL-METAL FRICTION. JOUr. Soil Sei. 7: 235-241, illus. (329) 1956. THE RELATIONSHIP BETWEEN THE MECHANICAL PROPERTIES OF SOIL AND THE PERFORMANCE OF SIMPLE CULTIVATION IMPLE- MENTS. Jour. Agr. Engin. Res. 1: 23-50, illus. (330) 1956. WINCH SPRAG DESIGNED TO UTILIZE SOIL FRICTION. JOUr. Agr. Engin. Res. 1: 51-55, illus. (331) and FOUNTAINE, E. R. 1954. THE MECHANISM OF SCOURING FOR CULTIVATION IMPLEMENTS. Nati. Inst. Agr. Engin. Tech. Memo. 116, 11 pp., illus. (332) and TANNER, D. W. 1959. THE RELATIONSHIP BETWEEN RAKE ANGLE AND THE PERFORM- ANCE OF SIMPLE CULTIVATION IMPLEMENTS. Jour. Agr. Eugiu. Res. 4: 312-325, illus. (333) PEATTIE, K. R., and SPARROW, R. W. 1954. THE FUNDAMENTAL ACTION OF EARTH PRESSURE CELLS. JOUr. Mech. Of Phys. of Solids. 2: 141-155, illus. (334) PFOST, H. B. 1948. ANALYSIS OF GEOMETRICAL DESIGN FACTORS INFLUENCING SOIL MOVEMENT OVER PLOW MOLDBOARD SURFACES. M. S. ThesiS, Auburn Univ., 49 pp., illus. (335) PHILLIPS, J. R. 1961. THE POWERED VEHICULAR WHEEL PLANE-ROLLING IN EQUILIB- RIUM : A CONSIDERATION OF SLIP AND ROLLING RESISTANCE. 1st Internatl. Conf. Mech. Soil-Vehicle Systems Proc. (Tu- rin), pp. 540-557, illus. (336) PiLLSBURY, R. D., JR. 1960. APPLICATIONS OF FLUOROCARBON RESINS IN FARM EQUIPMENT. Agr. Engin. 41: 802-803, 825, 826, illus. (337) PLANTEMA, G. A. 1953. SOIL PRESSURE CELL AND CALIBRATION EQUIPMENT. 3rd In- ternatl. Conf. Soil Mech. and Found. Engin. Proc (Zurich) 1: 283-288, illus. (338) POLLARD, W. S., JR. 1951. SOIL KNOWLEDGE CAN PROVE USEFUL TO DESIGNERS. S.A.E. Jour. 59 (9) : 39^1, 50, illus. (339) RADFORTH, N. W. 1961. LAND FACTORS AND VEHICLE DESIGN IN OPERATIONS ON ORGANIC TERRAIN. 1st Internatl. Conf. Mech. Soil-Vehicle Systems Proc. (Turin), pp. 158-170, illus. 478 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE (340) RANDOLPH, J. W. 1926. TRACTOR LUG STUDIES ON SANDY SOIL. Agr. Engin. 7: 178- 184, illus. (341) and REED, I. F. 1938. TESTS OF TILLAGE TOOLS. II. EFFECTS OF SEVERAL FACTORS ON THE REACTIONS OF FOURTEEN-INCH MOLDBOARD PLOWS. Agr. Engin. 19: 29-33, illus. (342) RATH JE, J. 1932. THE CUTTING OF SAND. Engineering 134: 116-118, illus. (343) REAVES, C. A. 1961. SIMILITUDE OF PLANE CECISELS IN ARTIFICIAL SOILS. Amer. Soc. Agr. Engin. Trans. 9: 147-150, illus. (344) and COOPER, A. W. 1960. STRESS DISTRIBUTION IN SOILS UNDER TRACTOR LOADS. Agr. Engin. 41: 20-21, 31, illus. (345) and NICHOLS, M. L. 1955. SURFACE SOIL REACTION TO PRESSURE. Agr. Engin. 36: 813- 816, 820, illus. (346) REDSHAW, S. C. 1954. A SENSITIVE MINIATURE PRESSURE CELL. Jour. Sei. Inst. 31: 467-469, illus. (347) REECE, A. R. 1961. A THREE POINT LINKAGE DYNAMOMETER. Jour. Agr. EugiU. Res. 6: 45-50, illus. (348) REED, I. F. 1940. RESULTS OF LEGUME COVERAGE STUDIES. Agr. Eugiu 21 * 129- 130, 134, illus. (349) 1940. A METHOD OF STUDYING SOIL PACKING BY TRACTORS. Agr. Engin. 21: 281-282, 285, illus. (350) 1941. TESTS OF TILLAGE TOOLS. IIL EFFECT OF SHAPE ON THE DRAFT OF 14-INCH MOLDBOARD PLOW BOTTOMS. Agr. Eugiu. 22: 101- 104, illus. (351) 1944. SOME FACTORS AFFECTING DESIGN OF TILLAGE MACHINERY AND PROPOSED APPROACH TO THEIR EVALUATION. Soil Sci. Soc. Amer. Proc. 9: 233-235, illus. (352) 1948. PLOW SECTION STUDIES. Nati. Tillage Mach. Lab. (Auburn Ala.) Ann. Rpt. (353) 1948. BASIC STUDIES OF DISK BLADES FOR AGRICULTURAL IMPLEMENTS. Nati. Tillage Mach. Lab. (Auburn, Ala.) Ann. Rpt. (354) 1958. TRACK STUDIES. Nati. Tillage Mach. Lab. (Auburn, Ala.) Ann. Rpt. (355) 1958. MEASUREMENT OF FORCES ON TRACK TYPE TRACTOR SHOES. Amer. Soc. Agr. Engin. Trans. 1: 15-18, illus. (356) 1962. THE EFFECTS OF INFLATION PRESSURE, LOAD, AND DRAWBAR PULL ON AXLE HEIGHT AND ROLLING RADIUS OF SIX TIRES. Amer. Soe. Agr. Engin. Trans 5: 125, 132, illus. (357) and BERRY, M. O. 1946. TESTS COMPARING PLOW BOTTOMS. Nati. Tillage Mach. Lab. Ann. Rpt, Auburn, Ala. (358) COOPER, A. W., and REAVES, C. A. 1959 EFFECTS OF TWO-WHEEL AND TANDEM DRIVE TRACTION AND SOIL COMPACTING STRESSES. Amer. Soc. Agr. Engin. Trans 2- 22-25, illus. * ' (359) and GORDON, E. D. 1951. DETERMINING THE RELATIVE WEAR RESISTANCE OF METALS. Agr. Engin. 32: 9^-100, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 479

(360) and MCCREERY, W. F. 1954. EFFECTS OF METHODS OF MANUFACTURE AND STEEL SPECIFICA- TIONS ON THE SERVICE OF DISKS. Agr. Engin. 35: 91-94, 97, illus. (361) REAVES, C. A., and SHIELDS, J. W. 1953. COMPARATIVE PERFORMANCE OF FARM TRACTOR TIRES WEIGHTED WITH LIQUID AND WHEEL WEIGHTS. Agr. Engin. 34: 391- 395, 399, illus. (362) and SHIELDS, J. W. 1950. FARM TRACTOR TIRE TESTS. V. 2, Nati. Tillage Mach. Lab. (Auburn, Ala.) Rpt. (363) REEVE, R. C, BOWER, C. A., BROOKS, R. H., and GSCHWEND, F. B. 1954. A COMPARISON OF THE EFFECTS OF EXCHANGEABLE SODIUM AND POTASSIUM UPON THE PHYSICAL CONDITION OF SOILS. Soil Sei. Soc. Amer. Proc. 18: 130-132, illus. (364) RICHARDS, L. A. 1953. MODULUS OF RUPTURE OF SOILS AS AN INDEX OF CRUSTING OF SOIL. Soil Sei. Soc. Amer. Proc. 17: 321-323, illus. (365) 1958. A THERMOCOUPLE FOR VAPOR PRESSURE MEASUREMENT IN BIO- LOGICAL AND SOIL SYSTEMS AT HIGH HUMIDITY. ScieUCe 128 : ^ 1084-1090, illus. (366) RICHARDS, S. J., WEEKS, L. V., and WARNEKE, J. E. 1960. COMPACTED BULK DENSITY AND HYDRAULIC CONDUCTIVITY FOB INDICATING THE STRUCTURAL STATUS OF SOILS. 7th lutematl. Cong. Soil Sei. Trans. (Madison, Wis.) 1: 249-255, illus. (367) RICHARDSON, R. 1958. SOME TORQUE MEASUREMENTS TAKEN ON A ROTARY CULTIVATOR. Jour. Agr. Engin. Res. 3: 66-68, illus. (368) RiCHEY, C. B. 1961. MOLDBOARD PLOWS. In Agricultural Engineer's Handbook, pp. 128-137, illus. New York. (369) ROAD RESEARCH LABORATORY. 1959. SOIL MECHANICS FOR ROAD ENGINEERS. 541 pp., illUS. [Gt. Brit.] Dept. Sei. and Indus. Res., Hammondsworth, England. (370) 1961. PERSONAL COMMUNICATION. [Gt. Brit.] Dept. Sei. and Indus. Res., Hammondsworth, England. (371) ROGERS, O. J. J. 1955. SOIL LOADS ON PLOUGH BODIES. PART I. METHODS OF MEASURE- MENT. Nati. Inst. Agr. Engin., Tech. Memo. 105, 12 pp., illus. (372) and TANNER, D. W. 1955. MEASUREMENTS WITH STRAIN GAUGES AT THE N.I.A.E. PART I. Nati. Inst. Agr. Engin. Tech. Memo. 106, 11 pp., illus. (373) ROLLO, C. A. 1947. AN ANALYSIS OF CERTAIN FACTORS AFFECTING TRACTION OF FARM TIRES. M.S. Thesis, Auburn Univ., illus. (374) Ross, I. J., and ISAACS, G. W. 1961. FORCES ACTING IN STACKS OF GRANULAR MATERIALS. Part I. Amer. Soc. Agr. Engin. Trans. 4: 92-96, illus. (375) RowE, R. J. 1959. EFFECT OF SPEED ON THE ELEMENTS OF DRAFT OF A SIMPLE TIL- LAGE TOOL. M.S. Thesis, Iowa State Univ., 94 pp., illus. (376) and BARNES, K. K. 1961. INFLUENCE OF SPEED ON ELEMENTS OF DRAFT OF A TILLAGE TOOL. Amer. Soc. Agr. Engin. Trans. 4: 55-57, illus. (377) RUSSELL, M. B. 1959. PLANT RESPONSES TO DIFFERENCES IN SOIL MOISTURE. Soil Sci. 88: 179-183, illus. (378) SARCINELLI, S. 1957. [EXPERIMENTS ON FARM TRACTORS. II. THE PIRELLI PATTERN 281.] [Italy] Cent. Naz. Mece. Agr. (Turin) 2: 75-86 (1956-1957), illus. 480 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

(379) SCHäFER, E. 1961. [INVESTIGATIONS ON THE SEPARATION OF POTATOES AND STONES BY MEANS OF ROTATING BRUSHES.] Landtechiiische Forsch. (Munich) 11: 170-175, illus. (380) SCHäFER, R. L. and LOVELY, W. G. 1963. AN AUTOMATIC-RECORDING SOIL SURFACE PROFILE METER. Amer. Soc. Agr. Engin. Paper 63-146. (381) SCHLESINGER, F. 1958. [FORCE MEASUREMENTS ON RIDGING BODIES.] Inst. Landtech- nische ( Potsdam-Bornim ) PubL 12, illus. (382) SELIG, E. T. 1962. DETECTION OF TRANSIENT STRESSES AND STRAINS IN SOIL. Sympos. on Detection of Underground Objects, Materials and Properties Proc. pp. 163-170, Ft. Belvoir, Va. (383) and ROWE, R.D. 1960. A STUDY OF ARTIFICIAL SOILS. Armour Res. Found. Rpt. 8920-14, 98 pp., illus. (384) SEUSER, K. 1955. [FOUR WHEEL DRIVE, STEERING BRAKES AND DIFFERENTIAL LOCK FOR TRACTOR PLOUGHING ON A SLOPE.] Laudtechnische Forsch. (Munich). 5: 1-5, illus. [Nati. Inst. Agr. Engin., Eng. Translation 14.] (385) SHIROKOV, B. I. 1954. [PROBLEM OF THE UTILIZATION OF ELECTRO-OSMOSIS OF SOIL IN PLOWING.] Zhur. Tekh. Fiz. 24: 1474-1482, illus. [U.S. Dept. Agr. Eng. Translation A 888.] (386) SHKURENKO, N. S. 1960. [EXPERIMENTAL DATA ON THE EFFECT OF OSCILLATION ON THE CUTTING RESISTANCE OF SOIL. (Jour. Agr. Eugiu. Res. 5- 226-232, illus. Eng. Translation.) (387) SILVER, W. H. 1960. DISCUSSION OF DESIGN FACTORS IN A SPRING TRIP BEAM AS- SEMBLY FOR MOLDBOARD PLOWS. Auier. Soc. Agr Engin Trans. 3 (2) : 63. (388) SiNEOKOv, G. N. 1952. [MOVEMENT IN THE SOIL OF THE WORKING PARTS OF SOIL CUL- TIVATING MACHINES IN THE INITIAL STAGE OF OPERATION.] Sel'khozmashina 3: 5-10, illus. [Off. Tech. Serv Eng Translation 60-21119.] (389) SKALWEIT, H. 1955. [INFLUENCE OF THE FORCES AT THE PLOUGH ON THE TRACTOR WITH 3-POiNT LINKAGE.] Laudtechuische Forsch. (Munich) 3: 6-11, illus. (Nati. Inst. Agr. Engin., Eng. Translation

(390) SKROMME, A. B. 1950. A BELT MOLDBOARD PLOW. Agr. Engin. 31: 387-390, illus (391) SMERDON, E. T., and BEASLEY, R. P. 1959. THE TRACTIVE FORCE THEORY APPLIED TO STABILITY OF OPEN CHANNELS IN COHESIVE SOILS. Mo. Agr. Expt. Sta Res Bui. 715, 36 pp., illus. (392) SMITH, H. P. 1948. FARM MACHINERY AND EQUIPMENT. Ed. 3. 520 pp illus New York. ' (393) SMITH, J. C. 1955. MIXING CHEMICALS WITH SOIL. Indus. and Engin Chem 47 • 2240-2244, illus. (394) SOEHNE, W. 1952. [THE DEFORM ABILITY OF ARABLE SOILS.] Grundlagen der Landtechnik 3: 51-59, illus. (395) 1952. [POWER TRANSMISSION BETWEEN TRACTOR TIRES AND ARABLE SOILS.] Grundlagen der Landtechnik 3: 75-87, illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 481

(396) 1953. [PRESSURE DISTRIBUTION IN THE SOIL AND SOIL DEFORMATION UNDER TRACTOR TIRES.] Grundlagen der Landtechnik 5: 49- 63, illus. (397) 1953. [FRICTION AND COHESION IN ARABLE SOILS.] Grundlagen der Landtechnik 5: 64-80, illus. (398) 1956. [SOME PRINCIPLES OF SOIL MECHANICS AS APPLIED TO AGRI- CULTURAL ENGINEERING.] Grundlagen der Landtechnik 7: 11-27, illus. (Nati. Inst. Agr. Engin. Eng. Translation 53.) (399) 1957. [INFLUENCE OF THE SHAPE AND ARRANGEMENT OF THE TOOL UPON THE DRIVING TORQUE IN ROTARY CULTIVATORS.] Grund- lagen der Landtechnik 9: 69-87, illus. (400) 1957. [IMPROVEMENT OF TRACTOR STEERING ON SIDE SLOPES BY MEANS OF DISC COULTERS.] Grundlagen der Landtechnik 9: 113-118, illus. (401) 1958. FUNDAMENTALS OF PRESSURE DISTRIBUTION AND SOIL COMPAC- TION UNDER TRACTOR TIRES. Agr. Eugiu. 391 276-281, 290, illus. (402) 1959. [INVESTIGATIONS ON THE SHAPE OF PLOUGH BODIES FOR HIGH SPEEDS.] Grundlagen der Landtechnik 11: 22-39, illus. (Nati. Inst. Agr. Engin., Eng. Translation 87.) (403) 1960. SUITING THE PLOW BODY SHAPE TO HIGHER SPEEDS. Grund- lagen der Landtechnik 12: 51-62, illus. [Nati. Inst. Agr. Engin, Eng. Translation 101.] (404) CHANCELLOR, W. J., and SCHMIDT, R. H. 1959. SOIL DEFORMATION AND COMPACTION DURING PISTON SINKAGE. Amer. Soc. Agr. Engin. Trans. 5: 235-239. 1962.] (405) and EGGENMULLER, A. 1959. [FAST-RUNNING ROTARY CULTIVATORS AND SLOW-RUNNING DIG- GERS : INVESTIGATIONS ON INDIVIDUAL TOOLS.] Grundlagen der Landtechnik 11: 72-80, illus. Nati. Inst. Agr. Engin. Eng. Translation 111.] (406) and THIEL, R. 1957. [TECHNICAL PROBLEMS WITH ROTARY CULTIVATORS.] Grund- lagen der Landtechnik 9: 39-49, illus. (407) SOURISSEAU, J. H. 1935. [DETERMINATION AND STUDY OF PHYSICO-MECHANICAL PROPER- TIES OF SOIL.] Organ, and Raps, du II Cong. Internatl. de Genie Rural (Madrid), pp. 159-194, illus. (408) SOUTHWELL, P. H. 1964. AN INVESTIGATION OF TRACTION AND TRACTION AIDS. Amer. Soc. Agr. Engin. Trans. 7: 190-193, illus. (409) STANILAND, L. N. 1959. FLUORESCENT TRACER TECHNIQUES FOR THE STUDY OF SPRAY AND DUST DEPOSITS. Jour. Agr. Engin. Res. 4: 110-125, illus. (410) STAUFFER, L. H. 1927. MEASUREMENT OF PHYSICAL CHARACTERISTICS OF SOILS. SOIL Sei. 24: 373-379, illus. (411) STEINBRUEGGE, G.- W. 1961. THE IDEAL TRACTIVE EFFICIENCY OF SOILS. 1st Internatl. Conf. Mech. Soil-Vehicle Systems Proc. (Turin) pp. 558-566, illus. (412) STEWART, A. 1948. A TUMBLING TEST FOR PRESSED PELLETS. Jour. Sci. lUSt. 25 : 438-440, illus. 482 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

(413) STOCKKLAUSNER, F., and LEHMAN, W. A. 1950. [SOIL COMPACTION DAMAGE.] Tech. fur Bauern und Gartner, Ausg. A2: 616-617, illus. (414) STONE, A. A., and WILLIAMS, I. L. 1939. MEASUREMENT OF SOIL HARDNESS. Agr. Engin. 20: 25-26, illus. (415) STURENBURG, P. 1957. [INVESTIGATIONS ON AIR-INFLATED ROLLERS FOR BREAKING OF CLODS IN POTATO HARVESTERS.] Landbauforschuug Volken- rode 7 (2) : 42-45. [Eng. Translation Jour. Agr. Engin. Res. 4: 88-90, 1959.] (416) SUN, H. Y., VAVRA, J. P., and CASTER, A. B. 1961. EFFECT OF SEVERAL INORGANIC AND ORGANIC MATERIALS ON CRUSTING OF CLAYPAN SOILS. Agrou. Abs. 53: 54. (417) SWIETOCHOWSKI, B., BORS, J., and PRZESTALSKI, S. 1959. [TESTS ON THE MEASUREMENT OF SMALL DISPLACEMENTS IN SOIL BY MEANS OF GAMMA RAYS.] Zesz. Nauk. Wyz. Szkol. Roln. Breslau. Roln. 7: 107. (418) TAKABEYA, F. 1932. THE INTERNAL MOTION OF SAND. Engineering 133: 148-149, illus. (419) TANNER, D. W. 1960. FURTHER WORK ON THE RELATIONSHIP BETWEEN RAKE ANGLE AND THE PERFORMANCE OF SIMPLE CULTIVATION IMPLEMENTS. Jour. Agr. Engin. Res. 5: 307-315, illus. (420) TANQUARY, E. W., and CLYDE, A. W. 1957. NEW PRINCIPLE IN TRACTOR HITCH DESIGN. Agr. Engin 38' 88-93, illus. (421) TAYLOR, D. W. 1948. FUNDAMENTALS OF SOIL MECHANICS. 700 pp., illus. New York. (422) TAYLOR, P. A., and WILLIAMS, N. Y. 1959. TRACTION CHARACTERISTICS OF 11-36 AGRICULTURAL TRACTOR TYRES ON HARD SURFACES. Jour. Agr. Engin. Res. 4: 3-8, illus. (423) TAYLOR, S. A. and Box, J. E. 1961. INFLUENCE OF CONFINING PRESSURE AND BULK DENSITY ON SOIL WATER MATRIC POTENTIAL. Soil Sci. 91: 6-10, illUS. (424) TELISCHI, B. 1962. SPRING TOOTH PROFILE DEVELOPMENT. Amer. Soc. Agr. Engin Trans. 5: 204-206, 209. illus. (425) McCoLLY, H. F., and ERICKSON, E. 1956. DRAFT MEASUREMENT FOR TILLAGE TOOLS. Agr. Eugiu 37 * 605-608, 617, illus. (426) TERRY, C. W., and WILSON, H. M. 1953. THE SOIL PENETROMETER IN SOIL COMPACTION STUDIES Agr Engin. 34: 831-834, illus. (427) TERZAGHI, K, and PECK, R. B. 1948. SOIL MECHANICS IN ENGINEERING PRACTICE. 566 pp. illus. New York. (428) THEINER, J. 1958. [INVESTIGATIONS INTO THE STATIC COMPACTION PROCESSES WITH SMOOTH ROLLERS.] Forscharb. Strwes. 37: 30-41, illus. (429) THOMPSON, J. L., and KEMP, J. G. 1958. ANALYZING DISK CUTS GRAPHICALLY. Agr. Engin. 39* 285- 287, illus. (430) TIMOSHENKO, S., and GOODIER, J. N. 1951. THEORY OF ELASTICITY. Ed. 2, 506 pp., illus. New York. (431) TRABBIC, G. W., LASK, K. V., and BUCHELE, W. F., 1959. MEASUREMENT OF SOIL-TIRE INTERFACE PRESSURES Asr Engin. 40: 678-681, illus. (432) TRANSPORTATION RESEARCH COMMAND, FT. EUSTIS, VA. 1958. SCALED VEHICLE MOBILITY FACTOR? (SAND). First Interim Rpt. Proj. 9-97-40—000. House Task 4.2, 28 pp., illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 483

(433) 1960. SCALED VEHICLE MOBILITY FACTORS. Second Interim Rpt. Proj. 9R97-40-001-01, House Task 4.2, Ö4 pp., illus. (434) 1960. VTOL DOWNWASH IMPINGEMENT STUDY SURFACE EROSION TESTS. Transport. Res. Com. Tech. Rpt. 60-67, 174 pp., illus. (435) 1961. SCALE MODEL OF VEHICLES IN SOILS AND SNOWS. ReS. Tech. Memo. 33, 33 pp., illus. (436) TROUSE, A. C, and HUMBERT, R. P. 1961. SOME EFFECTS OF SOIL COMPACTION ON THE DEVELOPMENT OF SUGAR CANE ROOTS. Soil Sci. 91: 208-217, illus. (436) TRUITT, T. D., and ROGERS, A. E. 1960. BASICS OF ANALOG COMPUTERS, illus., New York. (438) TRULLINGER, R. W. 1924. RESEARCH IN AGRICULTURAL ENGINEERING 1923. Agr. Engin. 5: 107-111. (439) 1924. EVOLUTION AND PROGRESS OF AGRICULTURAL ENGINEERING AT THE AGRICULTURAL EXPERIMENT STATIONS. Agr. EugiU. 5 ! 276-279. (440) 1925. SOIL COLLOIDS AND TILLAGE. Agr. Eugiu. 6: 61-63, 84-87. (441) 1926. RESEARCH IN AGRICULTURAL ENGINEERING—1925. Agr. Engin. 7: 279-282. (442) TURNBULL, W. J., JOHNSON, S. J., and MAXWELL, A. A. 1949. FACTORS INFLUENCING COMPACTION OF SOILS. Nat'l. Res. Council Highway Res. Board Bui. 23, illus. (443) TYURIN, I. V. 1957. THE MAL'TSEV SYSTEM OF CULTIVATION. Soils and Fert. 20: 305-309. (444) UFFELMANN, F. L. 1956. VEHICLE MOBILITY RESEARCH IN THE UNITED KINGDOM. Land Locomotion Lab. (Detroit) Res. Rpt. 3, pp. 5-19, illus. (445) UMEDA, S. 1958. CHARACTERISTICS OF SOIL RESISTANCE OF ROTARY TILLAGE TINES. Univ. Osaka [Japan] Bui., Ser. B, v. 8, pp. 9-17, illus. (446) UNITED STATES DEPARTMENT OF AGRICULTURE. 1938. SOILS AND MEN. U.S. Dept. Agr. Yearbook 1938. 1232 pp., illus. (447) 1951. SOIL ^SURVEY MANUAL. U.S. Dept. Agr., Agr. Handb. 18, 503 pp., illus. (448) 1954. DIAGNOSIS AND IMPROVEMENT OF SALINE AND ALKALI SOILS. U.S. Dept. Agr., Agr. Handb. 60, 160 pp., illus. (449) , Soil Survey Staff. 1960. SOIL CLASSIFICATION SYSTEM. 265 pp., illUS. (450) UNITED STATES DEPARTMENT OF THE INTERIOR, BUREAU OF RECLAMATION. 1960. EARTH MANUAL. 751 pp., illus. Denver. (451) VAIGNEUR, H. O. 1959. LOADING CHARACTERISTICS OF PLASTIC LINED MOLE DRAINS. M. S. Thesis, Clemson College, illus, (452) VAN BAVEL, C. H. M. 1949. MEAN WEIGHT-DIAMETER OF SOIL AGGREGATES AS A STATISTICAL INDEX OF AGGREGATION. Soil Sci. Soc. Amer. Proc. 14: 20- 23, illus. (453) 1960. SOIL DENSITY MEASUREMENT WITH GAMMA RADIATION. 7th Internatl. Cong. Soil Sci. Trans. 1: 284-289, (Madison, Wis.) illus. (454) UNDERWOOD, N., and RAGER, S. R. 1957. TRANSMISSION OF GAMMA RADIATION BY SOILS AND SOIL DEN- siTOMETRY. Soil Sci. Soc. Amcr. Proc. 21: 588-591, illus. 484 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

(455) VANDEN BERG, G. E, 1961. ANALYSIS OF FORCES ON TILLAGE TOOLS. U.S. Nati. Tillage Mach. Lab. (Auburn, Ala.) Ann. Rpt. (456) 1962. CONTINUOUS ANALOG TECHNIQUES IN EXPERIMENTAL RESEARCH. Paper presented South. A.gr. Workers Meeting, Jacksonville, Fla., 7 pp., illus. (457) 1962. TRIAXIAL MEASUREMENTS OF SHEARING STRAIN AND COMPAC- TION IN UNSATURATED SOIL. Auier. Soc. Agr. Engin., Paper 62-648. (458) 1962. REQUIREMENTS FOR A SOIL MECHANICS. Amer. Soc. Agr. Engin. Trans. 4: 234-238. (459) BucHELE, W. F., and MALVERN, L. E. 1958. APPLICATION OF CONTINUUM MECHANICS TO SOIL COMPACTION. Amer. Soc. Agr. Engin. Trans. 1: 24-27, illus. (460) and GILL, W. R. 1962. PRESSURE DISTRIBUTION BETWEEN A SMOOTH TIRE AND THE SOIL. Amer. Soc. Agr. Engin. Trans. 5: 105-107, illus. (461) and REED, I. F. 1962. TRACTIVE PERFORMANCE OF RADIAL PLY AND CONVENTIONAL TRACTOR TIRES. Amer. Soc. Agr. Engin. Trans. 5: 126-129, 132, illus. (462) REED, I. F., and COOPER, A. W. 1961. EVALUATING AND IMPROVING PERFORMANCE OF TRACTION DE- VICES. 1st Internatl. Conf. Mech. Soil-Vehicle System Proc, (Turin), pp. 402-411, illus. (463) VASEY, G. H., and NAYLOR, I. T. 1958. FIELD TESTS ON 14-30 TRACTOR TYRES. Jour. Agr. Engin. Res 3: 1-8, illus. (464) and NAYLOR, I. T. 1958. FIELD TESTS ON 14-30 TRACTOR TYRES. II. STATISTICAL TREATMENT OF RESULTS. Jour. Agr. Eugin. Res. 3: 187-198, illus. (465) VETROV, YU. A. 1958. [FRICTION BETWEEN THE BLADE AND SOIL IN THE PROCESS OF CUTTING.] Nauch. Dokl. Vysshei Shkoly [Stroilestro] 2: 111-124, illus. [Eng. Translation J. Crearer Lib. RTS 1445] (466) VINCENT, E. T. 1961. PRESSURE DISTRIBUTION ON AND FLOW OF SAND PAST A RIGID WHEEL. 1st Internatl. Conf. Mech. Soil-Vehicle Systems Proc, (Turin), pp. 858-878, illus. (467) VoMOciL, J. A., FouNTAiNE, E. R., and REGINATO, R. J. 1958. THE INFLUENCE OF SPEED AND DRAWBAR LOAD ON THE COM- PACTING EFFECT OF WHEELED TRACTORS. Soil Sci. Soc. Amer Proc. 22: 178-180, illus. (468) and WALDRON, L. J. 1962. EFFECT OF MOISTURE CONTENT ON TENSILE STRENGTH OF UN- SATURATED GLASS BEAD SYSTEMS. Soil Sci. Soc. Amer Proc 26: 409-412, illus. (469) WALDRON, L. J., and CHANCELLOR, W. J. 1961. SOIL TENSILE STRENGTH BY CENTRIFUGATION. Soil Sci Soc Amer. Proc. 25: 176-180, illus. (470) WANN, R. L., and REED, I. F. 1962. STUDIES OF TRACTOR TIRE TREAD MOVEMENT. Amer Soc Agr Engin. Trans. 5: 130-132, illus. (471) WARLAM, A. A. 1946. STRESS-STRAIN AND STRENGTH PROPERTIES OF SOILS. D. SC Thesis, Harvard Univ., illus. (472) WATERWAYS EXPERIMENT STATION, VICKSBURG, MISS. 1948. DEVELOPMENT OF TESTING INSTRUMENTS. Tech. Memo 3-240 Trafficability of Soils, 3rd Sup. 66 pp., illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 485

(473) 1950. MISCELLANEOUS LABORATORY TESTS. Tech. Memo. 3-271, Soil Compaction Investigation Report 5, 37 pp., illus. (474) 1950. TESTS ON TOWED VEHICLES. Tech. Memo. 3-240, 7th Sup. 109 pp., illus. (475) 1951. TRAFFiCABiLiTY OF SOILS, SLOPE STUDIES. Tech. Memo. 3- 240, 29 pp., illus. (476) 1952. TORSION SHEAR APPARATUS AND TESTING PROCEDURES. Bul. 38, 76 pp., illus. (477) 1953. UNIFIED SOIL CLASSIFICATION SYSTEM. Tech. Meuio. 3-357, V. 1, 30 pp ; V. 2, 11 pp. ; V. 3, 9 pp. (478) 1953. INVESTIGATIONS OF PRESSURES AND DEFLECTIONS FOR FLEXIBLE PAVEMENTS. Tech. Memo. 3-323, Rpt. 3, 13 pp., illus. (479) 1954. EFFECT OF SIZE OF FEET ON SHEEPSFOOT ROLLER. Tech. MemO. 3-271, Rpt. 6, 29 pp., illus. (480) 1954. INVESTIGATIONS OF PRESSURES AND DEFLECTIONS FOR FLEXIBLE PAVEMENTS. Tech. Memo. 3-323, Rpt. 4, Homogeneous Sand Test Section, 60 pp., illus. (481) 1955. PRESSURE CELLS FOR FIELD USE. Bul. 40, 33 pp., iUuS. (482) 1955. EFFECT ON SOIL COMPACTION OF TIRE PRESSURE AND NUMBER OF COVERAGES OF RUBBER-TIRED ROLLERS AND FOOT-CONTACT PRES- SURE OF SHEEPSFOOT ROLLERS. Tech. Mcmo. 3-271, Rpt. 7, 41 pp., illus. (483) 1958. STUDIES OF AERIAL CONE PENETROMETER. Tecll. Rpt. 3-462, Rpt. 2, 19 pp., illus. (484) 1959. DEFLECTION OF MOVING TIRES. Tech. Rpt. 3-516, Rpt. 1, 19 pp., illus. (485) 1959. INVESTIGATION OF EFFECTS OF 50,000-LB. WHEEL-LOAD TRAFFIC ON A SHALLOW-BURIED FLEXIBLE PIPE. Misc. Paper 4-364, 14 pp., illus. (486) 1959. A LIMITED STUDY OF SNAP-TRACKS. Misc. Paper 4-322, 8 pp., illus. (487) 1959. PILOT STUDY TO EVALUATE THE SQUEEZE TEST FOR USE IN VEHICLE MOBILITY RESEARCH. Misc. Paper 4-350, 15 pp., illus. (488) 1960. LIST OF PUBLICATIONS. 141 pp. (489) 1960. STRESSES UNDER MOVING VEHICLES. Tech. Rpt. 3-545, Rpt. 3, 33 pp., illus. (490) 1960. TRAFFICABILITY OF SNOW. Tech. Memo. 3-414, Rpt. 3, 65 pp., illus. (491) 1960. PETROGRAPHIC DATA ON BEACH, DUNE AND RIVER SANDS. MiSC. Paper 6-^08. (492) 1961. SOIL TRAFFICABILITY CLASSIFICATION SCHEME. Ist lutematl. Conf. Mech. Soil-Vehicle Systems Proc. (Turin), pp. 567- 574, illus. 486 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE (493) 1961. TESTS WITH RIGID WHEELS. Tech. Rpt. 3-565, Rpt. 1, 35 pp., illus. (494) 1961. TRAFFiCABiLiTY OF SOILS. Tech. Memo. 3-240, 16th Sup. 65 pp., illus. (495) 1962. ABSTRACTS OF REPORTS PUBLISHED BY ARMY MOBILITY RE- SEARCH CENTER TRAFFICABILITY AND MOBILITY RESEARCH. 22 pp. (496) 1965. WHEELS ON SOFT SOILS, AN ANALYSIS OF EXISTING DATA Tech. Kept. 3-670, 81 pp., illus. (497) WEAVER, H. A. 1950. TRACTOR USE EFFECTS ON VOLUME WEIGHT OF DAVIDSON LOAM Agr. Engin. 31: 182—183, illus. (498) and JAMISON, V. C. 1951. EFFECTS OF MOISTURE ON TRACTOR TIRE COMPACTION OF SOIL Soil Sei. 71: 15-23, illus. (499) WEBER, F. 1932. [INVESTIGATIONS ON THE INFLUENCE OF ELECTRIC CURRENT ON THE TRACTIVE FORCE REQUIRED IN PLOWING.] Thesis, Tech- nischen Hochscule, München, 47 pp., illus (500) WEIDENBAUM, S. S. /PtA-.^ TTT -^^^^\ ^/^^^^ o^ SOLIDS. Adv. in Chem. Engin. 11: 209-324, illus. (501) WELLS, A. A. 1950. THE DYNAMICS OF SOIL IN RELATION TO TILLAGE Ph D /r/.ox .xr „ Thesis, Cambridge Univ., England, illus. (502) WHITE, E. A. 1918. A STUDY OF THE PLOW BOTTOM AND ITS ACTION UPON THE ,^^^, FURROW SLICE. Jour Agr. Res. 12: 149-182, illus.

1918. A STUDY OF THE PLOW BOTTOM AND ITS ACTION UPON THE BURROW SLICE. Ph. D. Thesis, Cornell Univ., iilus (504) WiENEKE, F. 1955. THE MATHEMATICAL DETERMINATION OF THE RUNNING CHAR- ACTERISTICS OF A POWER-DRIVEN TRAILER. Laudtechnische Forsch. (Munich) 5: 26-29, illus. [Jour. Agr. Engin. Res 1: 101-105. 1956, Eng. Translation.] (505) WiLLETTS, B. F. 1954. THE PERFORMANCE OF FOOTINGS ON, AND CULTIVATION IM- PLEMENTS IN, SOILS. Ph. D. Thesis, Univ. of Durham England, illus. (506) WILSON, R. W. 1960. DISCUSSION OF DESIGN FACTORS IN A SPRING TRIP BEAM AS- SEMBLY FOR MOLDBOARD PLOWS. Amer. Soc. Agr. Engin Trans. 3(2): 64-65, illus. ^ ^ (507) WINKELBLECH, C. S. 1961. SOIL AGGREGATE SEPARATION CHARACTERISTICS OF SECONDARY /^no^ ^r TILLAGE TOOLS. M. S. Thesis, Ohio State Univ., illus. (508) WINTERKORN, H. F. 1936. SURFACE CHEMICAL FACTORS INFLUENCING THE ENGINEERING ^n^^r^Ti. T ^''íí: ^^^'^- ^^'- ^^^^^il' Highway Res. S.T 1^^*^ ^^^' ^^^^ P^^^C" (Washington, D.C.) pp. 293- 301, illus. (509) WOODRUFF, C. M. 1936. LINEAR CHANGES IN THE SHELBY LOAM PROFILE AS A FUNCTION /^-.^x ..r ^^ ®^^^ MOISTURE. Soil Sei. Soc. Amer. Proc. 1: 65-70 illus (510) WOODRUFF, N. P., and CHEPIL, W. S. ^. -L. OO íU, iiius. 1956. IMPLEMENTS FOR WIND EROSION CONTROL. Agr Euffin 37« 751-754, illus. & . oi . (511) CHEPIL, W. S ., and LYNCH, R. D 1957. EMERGENCY CHISELING TO CONTROL WIND EROSION Kans Agr. Expt. Sta. Tech. Bui. 90, 24 pp., illus. SOIL DYNAMICS IN TILLAGE AND TRACTION 487

(512) WooTEN, O. B., MCWHORTER, C. G., and RANNEY, C. D. 1962. UNDERGROUND APPLICATION OF HERBICIDE AND FUNGICIDES. Agr. Engin. 43: 30-32, 34, illus. (513) Wu HUNG-CHEIN. 1959. [THE EFFECT OF ELECTRO-OSMOSIS ON A DOUBLE-WHEEL-DOUBLE- PLOW IN PLOWING.] Acta Agr. Sinica 10: 135-137, illus. (514) YODER, R. E. 1937. THE SIGNIFICANCE OF SOIL STRUCTURE IN RELATION TO THE TILTH PROBLEM. Soil Sei. SOG. Amer. Proc. 2: 21-33, illus. (515) ZELENIN, A. N. 1950. [BASIC PHYSICS OF THE THEORY OF SOIL CUTTING.] 353 pp. illus. Moscow. (516) ZIMMERMAN, R. P., and KARDOS, L. T. 1961. EFFECT OF BULK DENSITY ON ROOT GROWTH. Soil Sei. 91 : 280-288, illus. 11. GLOSSARY

ACTION.—AU activities of an operating soil-force system. ACTIVE SOIL BEHAVIOR.—Specific actions in which the soil matrix moves. BEHAVIOR.—A specific action where the cause and effect (input and output) are uniquely related. BEHAVIOR EQUATION.—A mathematical relation that describes a specific action. BEHAVIOR PARAMETERS.—Parameters defined by behavior equations that assess behavior properties of soil. BEHAVIOR PROPERTIES.—Properties exhibited by soil in a behavior. COMPOSITE PARAMETERS.—Parameters that assess integrated rather than independent behavior properties of soil. DESIGN EQUATIONS.—Equations expressed in terms of design factors or parameters that describe the action of soil-machine systems. DESIGN FACTOR.—Geometric or operational entities that characterize machines in the action of a soil-machine system. DESIGN PARAMETER.—Parameters defined by design equations. DYNAMIC PARAMETERS.—Parameters defined by active behavior equations. DYNAMIC PROPERTIES.—Properties exhibited by soil in active behavior. EVALUATION.—The comparison of actual performance of a soil-machine system with desired performance or with a subjective standard. EVALUATION FACTOR.—Empirical index characterizing the degree to which the performance of a machine attains a desired level of performance. VEHICLE MOBILITY.— The movement of a specific vehicle over soil and terrain conditions in order to fulfill its intended mission. LAND LOCOMOTION.—The movement of a vehicle over land achieved by developing thrust from soil during crawling, walking, jumping, or rolling actions. MACROSHAPè.—The gross shape of soil contacting surfaces of a machine in a soil-machine system. MATERIAL PROPERTY.—A property that characterizes a soil material. MECHANICS.—Mathematical relations of forces and motions describing an action. MICROSHAPE.—The minute shape of macroshape elements of a soil-machine system—surface roughness or edge shape. PASSIVE SOIL BEHAVIOR.—Specific actions in which the soil matrix participates without movement. PASSIVE PARAMETER.—Parameter defined by a passive behavior equation. PERFORMANCE.—The products of the action of a soil-machine system including its efliciency. PERFORMANCE FACTOR.—A composite term of raeasures of performance developed for the purpose of establishing one numerical value of performance. SOIL.—A substance composed of air, water, organic matter, rocks, minerals, and products of their decomposition—the total soil. SOIL PHYSICAL CONDITION.—All physical characteristics, positions, distributions and properties of soil that are pertinent to its use. SOIL PHYSICAL PROPERTIES.—State and material properties of soil SOIL MATERIAL.—Solid mineral part of soil. SOIL PARAMETER.—A numerical quantity that describes the character or functional aspects of soil. STATE PROPERTY.—A property that characterizes the static state or condition of soil. SOIL REACTION.—The response of soil to application of forces. SUBSYSTEM.—A separate and distinct system that contributes to a more complex system. SYSTEM.—A hierarchy of components—forces, behaviors, subsystems or facts that are united and interdependent and form a coherent whole 488 GLOSSARY 489

TILLAGE ACTION.— The action of a soil-tillage tool system. TILLAGE EQUATION.—An equation that describes a tillage action. TRACTION ACTION.—The action of a soil-traction device system. TRACTION EQUATION.—An equation that describes a traction action. TRAFFICABILITY.—The capacity of a soil to support and withstand traffic. TRANSPORT.—The movement of loads over soil on nontraction devices such as runners, nonpowered w^heels, or tracks. 12. INDEX

Abrasion, by airborne soil, 106, 107 ; described, 52 ; factors affecting, 110, 112 ; mechanism, 109; of plastic plow covers, 235; parameters, 52; relation with modulus of rupture, 106 ; standard test for soil. 111 ; see also wear Acceleration, contribution to draft force, 318 ; in plow mechanics, 176 ; of soil by blade, 317 ; of soil in soil-tool mechanics, 130 ; see also speed Acceleration, soil, by moldboard plows, 228 Acceleration, tool, by increased forces, 213 Action, described by complete mechanics, 123; described by mechanics, 120; determined by interest, 120; influenced by soil-tool geometry, 191; parameters deñned by mechanics, 218 Active behavior, basis for use, 300 ; caused by dominant forces, 55 ; empirical, 102; measured, 334 Adhesion, apparent, 40; defined by equation, 90; description, 42; effect of angle of wetting, 48 ; effect of moisture tension, 45 ; effect of surface tension on, 44; effect of temperature on, 48; effect of wetting plow, 236; effect of sliding force, 162 ; effect on machine performance, 91 ; effect on tool filling, 252; equivalence of stress, 90, 162; equivalence of weight, 50; factors governing, 91; in soil-tool mechanics, 132, 141; interaction with friction, 49; measurement of, 44; Nichols' phases of friction, 51; on bulldozer blades, 252 ; on moldboard plows, 48, 176 ; on tires, 412 ; on tool edges, 244 ; related to physical properties, 89 ; scouring of plows, 91 ; soil body formation, 192 ; stickiness, 89 Aeration, required for plant growth, 303 Aggregates, behavior under stress, 305 Aggregate size, and cutting force, 209; see also clods Aggregate stability, method to assess, 105 Agricultural operation, cause compactness, 452 Agricultural system, hierarchy, 450; influenced by soil dynamics, 447 Air blast, to manipulate soil, 237 Air displacement, measure of volume strain, 30 Air plow, design, 236 All wheel drive, vehicles, 418 Analogs, applied to soil dynamics research, 458 Anchor, plant material in soil, 327 ; sprag in soil, 408 Angle, for minimum penetration resistance, 184; of soil body, 143; of shear surface, 131; of tool orientation, 256; penetrometer and relations, 187 Angle, ascending, defined, 170 Angle of bulldozing blades, effect on draft, 251 Angle of cutter, effect on soil deformation, 154 Angle of internal friction, determination of, 67-68 Angle of sharpness, effect on plow draft, 248 ; for tiller tines, 275 Angle of sliding friction, of soils, 51

490 INDEX 491 Angle of tool, effect on scouring, 178; soil confinement, 200 Angle of wetting, effect of surface roughness, 49; measurement, 48; soil solutions on metals, 49 Apparent coefficient of sliding friction, measurement, 49 Arch action, around stress transducers, 28; in compression chambers, 81; in granular materials, 24; in soil channels, 239; in tool action, 203; inñuence on traction performance, 405 ; observed in glass-sided box, 114 Artificial soils, to stabilize strength, 22 Area of contact, effect on adhesion, 47, 49 ; effect on penetrating force, 183 ; effect on plow performance, 237 ; effect on sticking, 93 ; measured for tires, 364 ; of cutters, 152 ; of tires, 365 ; tire footprint, 364 Area of influence, of grousers, 405 Auxilliary traction devices, performance, 410

Balloon, in soil volumeter, 30 ; to confine soil, 438 ; to measure soil compaction, 435 ; to measure soil rupture strength, 105 Bearing strength, estimated sinkage, 96; plate bearing test, 98 Behavior, active-passive interaction, 303; described for use, 120; effected by force application, 101 ; integrated influence, 304 ; interactions, 58 ; passive, 55 ; reduced to basic laws, 208 ; role of sub-behaviors, 120 ; subjective nature, 121 ; used in mechanics, 120 Behavior equations, as basic laws, 217 ; as integrating mechanics, 304 ; complexity, 120 ; determined by intended use, 306 ; developed for mechanics, 121 ; disregard in limited cases, 121 ; for compaction, 431 ; in tillage tool mechanics, 140; input-output, 57, 61; interactions in real systems, 301; initially empirical, 217 ; method to develop, 61 ; purpose, 59 ; represent behavior, 53 ; separation of mechanics, 62 ; to describe soil conditions, 301 ; use in mechanics, 117-118 Behavior parameters, effected by soil conditions, 61; identification, 64 Behavior properties, described by basic laws, 57 ; identified in mechanics, 119 ; related to material properties, 56 ; related to physical properties, 59 ; selected for interest, 300; study of, 60 Behavior relations, direct and indirect, 302 Bending failure, assumptions, 75 Bending moment, in furrow slice, 176 Bernstein equation, analysis for parameter, 99 ; for sinkage, 98 ; in vehicle mechanics, 348 Blade angle, changing in rotary tillers, 275 ; effect on bulldozer-draft force, 251 Blast mechanism, 108 Blast erosion, by fluids, 108; described, 105 Blast penetration, influence of energy on depth, 109 Blast stream, depth of penetration, 108 Braking action, of wheel, 371 Bulldozer blades, draft forces, 251 Bulldozing, soil transport, 250 Bulldozing resistance, of wheels, 351

Cage wheels, auxilliary traction devices, 412 Capacity of work, influence on performance, 336 Carcass, tire, stress distribution on, 361 Cells, pressure, see stress transducers Cemented soil, shear curve, 66 Center of gravity, of plow furrow, 206 492 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Channels, formed by tools, 239 Characteristics, of compaction behavior, 432 Characterization(s), by soil parameters, 53; fundamental and independent quantities, 54; of physical properties, 56; of tool edge shapes, 242; of tool shape, 219; of traction and transport devices, 355; of vehicle morphology, 416 Characterization of soil, in traction performance, 384 Chisel angle, and soil disturbance, 257 Chisel plow, draft and depth of operation, 261 Chisel speed, effect on clod size, 322 Clay, sliding friction, 50 Cleaning, effect of teeth on cutters, 294 ; of rotary tillers, 277 ; of tire lugs, 415 Clearance angle, effect on tool penetrations, 258; effect on tool forces, 197 Clod(s), effect of tool speed, 322; energy required to reduce size, 104; for erosion control, 322 ; measurement of strength, 73 ; movement in soil profile, 323; segregated by tillage tools, 323; sieve for separating, 319 Clod shatter, conditions influencing, 104 Clod size, and tool performance, 103 ; effect of size of cut, 263, 320, 338 ; effect of tillage speed, 322; efficiency of tillage tools in changing, 104; measured following plowing, 321; measure of pulverization, 103; method to express, 319; reduced by oscillating tools, 285 Clod strength, method to determine, 103 Coefficient of friction, equation, 40; in plow mechanics, 147; in traction equation, 408 Coefficient of sliding friction, average value, 166; composite parameters, 163; effect of moisture on, 236; effect of normal stress, 167; effect of sliding distance, 167; effect of scouring, 178; for polished tools, 234 Coefficient of traction, device to measure, 342; of radial-ply tires, 402; on ground materials, 386 Cohesion, defined by Coulomb's equation, 35; determination of, 67-68; effect on wind erosion, 106 ; estimated from vane shear data, 70 ; in tension failure, 38; in soil-tool mechanics, 141, 143; in situ measurement of, 75; measured in soils, 72; pre and post collapse, 101; residual, 71; to assess induced strength, 101; use in traction equation, 408 Cohesive parameter (K^), defined, 99 Compact soil, effect on plant roots, 444 Compaction, by machinery, 441 ; due to shrinkage, 442 ; effect on soil strength, 445; tillage objective, 309; see also compression Compaction behavior, characteristics of, 432, described, 431 ; of loose soils, 437 Compaction distribution, described, 442; see also stress distribution Compactive effort, influence on compactness, 440 Compatibility, behavior equations, 123, 302 Composite behavior, Bernstein equation, 100 Composite design factors, tire lugs, 396 Composite parameters, coefficient of friction, 163; defined, 63; development, 64; examples, 94; for wheels, 386; measurement of, 93; of tracks, 405; to simplify descriptions, 307 Complete mechanics, idealistic, 123 Complex behavior, description, 210 Compression, description of, 80-81 Compression failure, definition, 36; elastic and plastic, 432; in soil, 36; not independent of shear, 37 ; principle of measurement, 37 INDEX 493

Compressive strength, in penetration mechanics, 185 Compressive stress, effect on type of sample failure, 77 Condition of tool, effect on friction, 233 Conditioning of soil, tillage objective, 308 Cone index, measurement, 424 Cone penetrometer, to measure cone index, 424 Contact area, see area of contact Continuum model, to describe granular materials, 23-24 Continuum theory, applied to stress, 14 Control facilities, for soil dynamics research, 5-13; required for force measurements, 311 Control of plants, tillage objective, 309 Conventional small strain, definition, 17 Coordinate system, for rotary tools, 269; for tillage tools, 223; for vector analysis, 313; for vehicle slip, 346 Cost, of design, 418; of tillage, 211 Coulomb equation, deñned, 35 ; for soil friction, 40 ; in traction equation, 344 ; to describe adhesion parameters, 90 Coulomb theory, of shear, 34 Coulter, effect in interaction, 283; effect on stress distribution, 316; to handle plant materials, 327 Creep, soil, 185 ; tire deflection, 363 Crop production, effect of soil conditions, 430 Crop production management, nature of tillage operations, 454. Crushing, of soil particles. 111 Cutting, components of force, 151 ; definition of behavior, 209 ; described, 148 ; importance in torque requirements, 273; in soil-tool mechanics, 126-133; interactions, 150 Cutting angle, during rotary movement, 275 ; effect on work input, 276 Cutting force, effect of aggregate size, 209; effect of soil-tool geometry, 199; method of study, 190; reduced by oscillation, 280 Cutting resistance, effect of tool geometry, 201

Deflection, of tires, 362, 364 Deformability of apparatus, effect on sample strain, 77 Deformation modulus (K), defined, 72 Degree of confinement, effect of geometry, 199; effect on cutting resistance, 198; effect on soil cutting, 149 Dense soil, shear curve, 66 Depth control, parallel linkage, 259 ; radial linkage, 259 Depth of chiseling, effect on draft, 261 Depth of cut, effect of tool orientation, 239 ; effect on draft, 134, 291 ; effect on scraper performance, 254; to control weeds, 238 Depth of operation, effect on cutting force, 189, effect on draft force, 261; effect on shear surface angle, 136 Depth of plowing, effect of edge shape, 247; effect of stress distribution, 316 Depth : width ratios, effect on daft, 204 ; of tillage tools, 148 ; utilitarian value, 63 Design, based on force measurements, 318 ; evaluation of, 299 ; flexible tracks, 410; inadequacies, 300; interplay with performance, 299; optimizing interactions, 288; scraper bowls, 254; soil reactions, 208; soil-tool friction, 233; stress transducers, 27-28; subsoiler shapes, 231; tillage tools, 211; to effect 4:94 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE soil reaction to blades, 251; to improve beet extraction, 333; to improve scraper bowl filling, 255 ; tool wear, 249 ; traction and transport devices, 381 ; transport devices, 386; winch sprags, 409 Design equations, evaluation of relations, 217 ; interactions, 289 ; microshape, 233; need, 265; tillage tools, 212; tool descriptions, 255 Design factors, in design equations, 212, 276 ; operational control for traction, 416; wheels, 392 Design parameters, defined by equations, 218; for moldboard plows 227- identified, 385 Design principles, applied to multipowered tools, 266 Design variables, elements of classification, 4 ; in tillage relations, 212 Desired performance, based on use, 334; effect on evaluation, 336 Deviator stress, described, 16 Differential lock, effect on traction, 418 Differential slip, method to measure, 373 Digger plow, scouring, 92 Dimensional analysis, penetrometers, 185 ; soil dynamics research, 485 ; vehicle performance, 426 Direct shear, principles of measurement, 41 ; rock fragments, 68 ; soil truss, 68; typical relations, 66 Disk(s), position and wear, 249 Disk packers, anchor plant residues, 327 Disk wear, measured by weight loss, 249 Disturbed soil, by chisels, 261 Dominant forces, active behavior, 55 ; mechanical forces, 59 ; soil manipulation, 214 Double-cut plow, described, 290 Draft, calculated, 131 ; calculated and measured for cutter, 191 ; chisels, 331 ; cyclic nature, 314; different plows, 338; double-cut plow, 291; effect of cutting depth, 189 ; effect of depth of operation, 208 ; effect of oscillation, 284 ; effect of spacing of tools, 208 ; effect of tool angle, 330 ; effect of teeth spacing, 294 ; effect of wear, 247 ; equation for electro-osmosis, 268 ; flexible tines, 280; interactions in double-cut plow, 291; limiting in tool use 230; model bulldozer blades, 250; predicted by mechanics, 147; reduced by electro- osmosis, 267 ; reduced by multipower designs, 265 ; relation with unit stress, 314 ; soil-tool mechanics, 126-133, 143 ; subsoiler, 231 ; tillage tool 138 • tool interactions, 289 ' ' Dragline bucket, model study, 294 Drain liners, methods to install, 331 Drain opening, method to measure, 332 ; see also channel Drawbar pull, average performance, 380; calculated, 428; effect of hitch point, 407; maximum and slip, 380; measure of performance, 366; performance equation, 382; wheels, 371 Driven wheels, widespread use, 392 Drop-shatter, techniques described, 103 ; use in plow study, 338 Dual tires, performance, 414 Dyes, to study soil mixing, 325 Dynamic behavior, Bernstein equation, 98 ; see also active behavior Dynamic parameters, dependence on models, 62; determined by behavior equations, 60; in tillage equations, 216; in traction mechanics, 342- of induced strength, 101 ; of soil strength, 22 Dynamic properties, abrasion, 52; assessment, 63,- definition, 14; described, INDEX 495 53, 55, 61 ; elements of classification, 4 ; in gross behavior, 102 ; in mechanics, 123 ; in soil movement, 113 ; parameters, 14 ; principles to study, 61 Dynamic resultants, elements of classification, 4 Dynamic tools, defined, 270 Dynamometer, described, 312 ; tool forces, 318 ; track shoe forces, 351

Edgeshape, design, 249 ; described, 242 ; effect of wear, 245 ; effect on plowing depth, 247 ; effect on tool force, 243 ; effect on soil movement, 244 ; of tillage tools, 221 Effective stress, during impacts, 439; in shear tests, 73-74 Efficiency, different plows, 338 ; tillage tool cuts, 272 ; tractive devices, 374 Elastic deformation, during cutting, 158 Elastic theory, restricted to small strain, 20-21 Elasticity, coefficient, 157 Elasticity equations, to calculate stress distributions, 26 Electrical power, see power Electro-osmosis, to reduce adhesion, 269; requisite conditions, 268 Empirical behavior equations, development role, 217 Empirical mechanics, need, 63 Energy, basis of tool performance, 263; conserved by tool design, 325; effect of worn shares, 247 ; impacts on clod size, 321 ; in U.S. tillage, 220 ; in U.S. traction, 340 ; multiple sources for tools, 265 ; of blast streams, 109 ; possible savings in tillage, 452 ; required for actions, 298 ; required for traction, 374 ; to breakup soil, 263, 338 ; to shatter clods, 104 Environmental forces, effect on soil compactness, 431 ; effect on soil conditions, 302 Evaluation, based on desired performance, 336 ; basis for vehicle performance, 381; feedback for design, 299; of tillage for plant growth, 303; of tire performance, 400 ; of traction performance, 365, 379 ; of vehicle performance, 381 Evaluation factors, described, 337 Evaluation of performance, described, 334-339; principles, 299 Evaluation of tillage,* plow performance, 338 Evaluation of traction, comparative techniques, 385

Failure, complexity in soil, 32 ; criterion, 37 ; definition, 32 ; in traction device, 344 ; mechanics of in abrasion, 53 ; represented by models, 64 ; representative test devices, 64 ; surfaces, 34-35 ; see also yield Final soil conditions, in tillage equations, 213 ; produced by tillage, 212 Flexibility, of vehicles, 418 Flexible wheels, stress distribution under, 358 Fluid mechanics, in passive behavior, 304 ; to describe transmission actions, 58 Force(s), balance in implements, 297; defined by the wrench, 313; designation, 311 ; direction of resultants, 142, 153 ; disks in gangs, 249 ; effect of approach angle, 257 ; effect of plow share wear, 196 ; environmental, 302 ; evaluation of performance, 298; hypothetical thrust, 367; in behavior equations, 57; in soil-tool mechanics, 126-133; measured for performance, 310; measured on tillage tools, 318; methods of expressing, 313; methods of reporting, 311; methods to measure, 310-318; minimized by geometry, 184; minimum required, 296; on penetrometer, 183; on rigid wheels, 367; on segmented plow, 316; on sliding surface, 171-174; on sod plow, 174-176; on soil cutters, 151 ; on traction devices, 342, 409 ; on wheels, 352, 378 ; penetration AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE resistance, 185; resultant on tire, 367; sequences in tillage, 297; to compact soil, 432; to cut soil, 191; to extract root crops, 333; to manipulate soil, 212- traction equation, 382 ; see also draft, drawbar pull, thrust, weight Force(s), tool, contributions by shear, friction, acceleration, 318 Force application, control by design, 297; principles of, 295; timed for manipulation, 297 Force systems, applied to soil, 55 Four wheel drive, see all wheel drive Friction, effect of polytetrafluoroethylene, 235 ; effect of weight, 51 ; effect on sample compaction, 81; equation, 40; in soil-tool mechanics, 126-133 141- in soil reactions, 86; incipient failure, 41; measures, 88; Nichols' phases' 51; observed behavior, 41; on blades, 317; see also sliding friction Friction angle {\p), principles of measurement, 87 Friction apparatus, description, 88 Friction models, for soil, 41 Frictional parameter (K0), defined, 99 Full cut section, plow shape parameter, 225 Functional relations, design equations, 212, 220 Furrow wall, soil confinement, 200

General purpose plow, scouring, 92 Geometric parameters, for tillage tools, 216; for traction devices, 349 364 388 Geometry, of penetrometers, 184 Glass-sided box, method for measuring movement, 114 ; to observe shear 36 • to observe soil bodies, 194; to observe soil movement under tire lugs,'363,' to observe stress concentrations, 29 Graphical description, of disks, 292 Grip failure, in traction, 348 Gross behavior, importance of, 102 Ground conditions, effect on towing force, 387 ; effect on traction, 399 Ground effects machine, to reduce wheel loads, 418 Ground failure, in traction, 344 Grouser spacing, effect on traction, 405

Half tracks, effect on vehicle performance, 411 Hardness, to reduce tool abrasion, 53 Harrowing, to mix soil, 325 Hierarchy, of systems, 450 High speed plows, soil acceleration, 228 Hitch (es), linkage systems, 259; to control plow angle, 259; to transfer load to tire, 415 Hitch point, effect on tractive efficiency, 407

Ideal tractive efficiency, method to determine, 352 Identification of parameters, by direct observations, 385 Identification properties, material properties, 56 Implement, combined actions, 295; described, 288; shape description, 271 Implement design, effect on rotary tiller torque, 277 Implement geometry, graphical description, 292, rotary tiller, 272 Incipient failure, in triaxial shear, 71 Inclined tools, mechanics, 126 Independent parameters, coefficient of friction, 163; defined, 63; measurement, 64 INDEX 497

Indirect tension measuring, method, 76 Induced strength, described, 100 Inflation pressure, effect on stress distribution, 360 ; effect on tire deformation, 370; effect on tire performance, 413 Initial soil conditions, in tillage equations, 213 Instrumentation, for soil dynamics research, 485 Intended use, interacting systems, 303 Interactions, in design equations, 289; in double-cut plow, 290; mixed force system, 214; of behaviors in a mechanics, 119; of grousers, 406; of speed and oscillations, 286 ; of teeth on blades, 292 ; of tillage tools, 207 ; of tire design factors, 395 ; of tools in implements, 288, plow and coulter, 316 ; soil traction device, 343 Internal friction, angle defined by shear equation, 35

~~Jointers, to handle plant residue, 327 Jourgenson squeeze test, to measure shear stress, 85~~

~~Kneading compaction, shear and vibrate soil, 83; stresses, 439~~

Land forming, minimum tillage, 453 Land locomotion, agricultural requirement, 456 Largest principal stress, effect in soil compaction, 81, 433 Lift angle, effect on blade draft, 254; effect on chisel draft, 315; effect on draft, 134, 202, 317; effect on model dragline bucket draft, 294; effect on shear surface angle, 136; effect on soil reaction, 238 Limit analysis, to calculate stress distributions, 26-27 Lineal strain, measurement, 30 Load, effect on soil-metal contact, 93 ; load carrying index of vehicles, 376 Loading cycle, effect on soil compaction, 438; effect on soil strength, 86 Locomotion, objectives, 456 Loose soil, shear curve, 66 Lubrication, Nichols' phases of friction, 52 Lug(s), stress distribution on, 361 Lug angle, effect on tire performance, 398 Lug curvature, effect on traction, 398 Lug design, effect on tire performance, 393 ; studies, 395 ; field studies, 399 Lug direction, to promote cleaning, 415 Lug height, effect on tire performance, 396 ; effect on wheel performance, 394 Lug size, effect on traction force, 407 Lug spacing, effect on performance, 407; effect on tire performances, 397

Macroshape, of rotary tiller tines, 274; of tines, 271 Management techniques, applied to soil dynamics systems, 458 Material(s), installed in soil, 330 Material handling, tillage objective, 309 Material properties, and soil use, 300; described, 56; effect on behavior, 304 related to behavior properties, 56; role in compaction, 430 Mathematical descriptions, for design equations, 270 ; of moldboard plow, 222 of tool shape, 219 Mathematical model, determines behavior parameters, 62; for cutting, 158 representative of action, 64 Mathematical property, hypothetical values, 39 Maximum compaction, location under tires, 435 498 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Maximum shearing stress, effect on soil compactness 436 Mean normal stress, effect on compactness, 436; effec't on volume strain 82- invariant of stress tensor, 16; under moving vehicles, 443 Measuring device, model simulation, 64 Mechanical forces, action in compaction, 430; separated and defined 59 Mechanical impedance, of plant roots, 444 Mechanics, analysis of inadequacy, 131; for sliding actions, 171- of cutting 150-160; of traction devices, 341; phases of development, 121; principles for development, 120, 160; representative of behavior, 119; role in use of soil, 304; to calculate draft, 134; to define parameters, 218; use of behavior equations, 125 Metals, abrasion, 53, 109; adhesion, 93; hardness and wear. 111- wetting angle, 49 » > ^ Metals theory, model for soil yield, 31-32 Microshape, and wear, 198; effect on soil reaction, 252 Minimum tillage, goals, 453 Mixed force systems, behavior interactions, 57 ; interaction 214 Mixing, by harrowing, 325; effect of initial size, 323; method to study 325- tillage objective, 309 ^» » Mixing coefiicient, equation, 326 Mobility index, calculated for vehicles, 417 Model, to describe plow shape, 221 Modulus of elasticity, in assessment of bearing strengths, 97 Modulus of pulverization, to assess soil movement, 322 Modulus of rupture, equivalence to tensile test, 78; method to determine 75- relation with abrasion, 106 ' * Mohr circle, in evaluating shear stress, 67-68; to describe shear, 34-35 Mohr diagram, stresses during scouring, 179 Mohr stress theory, applied to tensile failure, 78 Moisture content, effect on electro-osmosis, 267; effect on tool interaction, 289 Moisture now, effect by soil compaction, 445 Moisture movement, effect on adhesion, 49 Moisture suction, see moisture tension Moisture tension, correction for effective shear stress, 74; effect on adhesion 45; effect on friction, 51; effect on soil strength, 444; equivalent soil strength, 85; equivalence to mechanical stress, 74; equivalence of strength, 80; linear relation with soil strength, 84; measurement during sliding 162- used to control normal stresses, 50 ' ' Moldboard plow, draft, 261; historical tests, 221, oscillated, 287; performance measured, 336 Mole channels, size, 239 Momentum, soil breakup, 40 Mulch, anchored on soil surface, 327 Multi-powered tools, see powered tools

Natural strain, definition, 18-20 Nonhomogeneity, of soil clods, 322 Nonrigid body movement, interactions, 40 Nonrolling traction devices, equations, 342 Normal stress, distribution on plow surface, 68; due to adhesion, 49; effect on abrading soil, 110; effect on friction, 40, 41; effect on sliding force, 162- effect on soil compaction, 434; effect on wear, 247; in Coulomb shear INDEX 499 equation, 34; interpreted as adhesion, 90; measurement, 27; on sliding surface, 166

Off-the-road, locomotion, 340 Operational control, of traction design factors, 413 Orientation, effect on blade angles, 239; method to express, 256; of rotary tiller tines, 274 ; of rotating tools, 269 ; stress transducers, 27, 362 Orientation of soil-tool system, effect of slope, 205 Oscillations, reviewed, 280; see also vibrations Oscillating tools, described, 279 ; effect on clod size, 285 ; power requirements, 282, 285 Oscillation frequency, effect on rate of cutting, 280 Oscillation parameters, relation with draft force, 286-287

Parameters, abrasion, 52 ; for soil-tool mechanics, 123 ; see also cohesion, friction, tool, tire Partial mechanics, development, 125; utility, 160 Particle size, coefficient of friction, 112 ; effect on abrasion, 106 ; effect on blast penetration, 108-109 ; effect on mixing, 323 ; effect on sliding path, 171 ; effect on wind erodability, 106 Passive behavior, basis for soil use, 300 ; transmitted force systems, 55 Passive earth pressure theory, in sprag equation, 408; in tillage tool mechanics, 139 Path of motion, drawn tools, 260 ; oscillating tools, 283 ; rotary tools, 275 Path of soil sliding, apparatus for tracing, 229 ; method to describe, 229 Path of tool travel, description, 269 Penetration, composite behavior, 181 Penetration force, calculated, 184 Penetration resistance, a composite property, 94; influenced by geometry, 182 Penetrometer(s), aerial, 95; impact parameter c, 94; recording, 95; static parameter, 94 ; tilting plate, 100 ; to assess soil conditions, 189 ; to characterize soil, 94 ; to predict plow draft, 96 ; to predict rolling resistance, 96, 424 ; to predict seedling emergence, 96; types, 94 Performance, based on clod size, 103 ; based on soil conditions, 336 ; calculated with mechanics, 298; criterion for tractive devices, 366; defined, 298; described, 298; measures, 377; measuring soil condition, 310; of material placement machines, 330; of moldboard plow, 336; of rotating plow, 336; of rotary tillers, 271; of spading machine, 336; of tillage tools for plant growth, 303; of traction devices, 365; of winch sprags, 409; qualitative descriptions, 299; specific goals, 300 Performance criterion, soil factors, 298 Performance factors, described, 337 Permanent deformation, as a yield criterion, 32 ; of soil, 21 Philosophy, for tillage, 454 Photo elasticity, use in soil, 29 Physical properties, changes described by mechanics, 304; circumvented by behavior equations, 63; effect on abrasion, 106; related to behavior properties, 59; relation with behavior, 30^308 Pi-terms, in dimensionless equations, 426 Pipe, installed by tillage, 331 Placement of plant residue, by plowing techniques, 328 500 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE

Plant growth, complex behavior relations, 302; so;l physical requirements, 300; soil plant dynamics, 451 Plant material, effect on soil strength, 330 Plant residue, anchored in soil by tillage, 327; effect on water movement, 328- handled by tillage, 326-330 ' Plant roots, effect of soil conditions, 57 ; impeded by compact soil, 444 ; severed by tillage, 238 Plastic deformation, during cutting, 158 Plastic flow, described, 39, 83 Plastic limits, related to soil strength, 83-85 ; to determine shear force, 84 Plastic theory, to describe stress-strain relations, 21 Plasticity, coefficient, 157 Plastics, see polytetrafluoroethylene Plows, descriptions, 221; force distribution on, 316; interaction with coulter 316; measurement of wear, 197; movement of soil, 114-115; sliding forces,'

Plow coulter, interactions, 289 Plow covering, plastic, 235 Plow description, graphic, 223-224; Jefferson's model, 221; White's analysis, 222 Plow design, equation, 226; single and double-cut, 291; to wet moldboard, 236 Plow draft, effect of edge shape, 248; effect of electro-osmosis, 268- effect of plowing depth, 260; effect of polytetrafluoroethylene, 235; effect of stones 160; effect of vibrations, 287; effect of width of cut, 262; equations for speed effects, 263.; mechanics for calculating, 175; reduced by moisture, 236- related to soil resistance, 96 ' * Plow furrow, center of gravity, 115; movement, 113 Plow orientation, controlled by hitching, 259 Plow parameters, for high speed plows, 227; in performance equations, 226 Plow performance, equation, 226 Plow scouring, effect of soil conditions, 233 Plow setting, effect on clod size, 321 Plow shape, analyzed by computer, 228; apparatus to measure, 223; correlated with use, 229; descriptive parameters, 227; photographic apparatus, 224; related to soil manipulation, 225 Plow share, apparatus for measurement, 198; effect of wear, 196; forces on, 316; method to study wear, 111; wear, 246 Plow speed, effect on path of soil travel, 228 Plow surface conditions, prevents scouring, 233 Plowing, effect of wear on depth, 247 ; to mix soil, 325 Pneumatic tires, effect on towing force, 387 Poisson's ratio, in assessment of bearing strength, 97 Polytetrafluoroethylene, as plow covering, 235; to'eliminate soil bodies 194- to reduce adhesion, 88 ' ' Porosity, effect of compaction, 435 Post-collapsed cohesion, deflned, 101 Power, for electro-osmotic plowing, 267; for oscillating tools, 282, 285- in draft equations, 267; limiting for tillage, 220; required for electro- osmosis, 266 Power efficiency, average for performance, 380; criterion of tire performance, 374; of radial-ply tires, 402 INDEX 501 Powered tools, design principles, 266 ; multipowered tools described, 265 ; oscillating, 279 Pre-collapsed cohesion, defined, 101 Prediction, vehicle performance, 420 Pressure transducers, see stress transducers Proportional loading, in compaction, 436 Pulverization, mechanism of failure, 103-104 Pulverization modulus, expression of clod size, 322 Pure cutting, not continuous action, 210 ; of rigid bodies, 159 Pure shear, determination of, 86 Push soil, described, 178

Radial-ply tires, described, 400; improved performance, 403 Radioactivity, to detect soil movement, 115, 242 ; to study wear, 111 ; to trace soil mixing, 325 Rating cone index, described, 424 Recurved disk, designed for coverage, 329 Relative cohesion (Crei), defined, 101; in soil-tool mechanics, 143 Remolding index, described, 424 Research, facilities for soil dynamics research, 5-13 ; for tractive devices, 395 ; goal in soil dynamics, 123 ; in soil dynamics, 447 ; in traction, 385 ; of tool interactions, 288; on increase for traction, 341 Residual cohesion (C^), defined, 71; measured in soils, 72 Rigid body movement, described, 39; displacement by cutters, 160; of soil in traction, 354 Rigid wheel, stress under, 357 Ring shear, determination of shear work, 72 ; equation for analysis of, 69-70 ; to measure friction, 164; to minimize errors, 69 Ring slider, to measure friction, 88 Rolling moldboards, to reduce adhesion, 237 Rolling radius, of deformable wheel, 372; of wheels, 370 Rolling resistance, coefficient of, 386; described, 351; effect of wheel parameters, 391; of flexible wheels, 386; of rigid wheels in sand, 388; of wheels on field soils, 389, prediction by penetrometer, 96, 424 Rolling tires, defiection, 364 Rolling traction devices, reference systems, 345 Root crops, force to extract, 333; separation from soil, 332 Rotary tiller, design factors, 269-279 ; effect on soil breakup, 321, Japanese, 279 Rotary tilling, to mix soil, 325 Rotating disks, effect on soil movement, 237 Rotating plow, performance, 338 Rotating tools, configurations, 270; described, 269; performance, 271 Rubber, coefficient of sliding friction, 165 Rudimentary mechanics, simplified actions, 209 Rupture, effect of soil texture, 105; in gross behavior, 103; measured by balloon technique, 105

Sand, sliding friction, 50 Scouring, definition, 176; effect of soil conditions, 233; factors affecting, 178; improved by electro-osmosis, 266 ; improved with plow covering, 194 ; on tool surface, 176 ; production of soil bodies, 192 ; stresses on surface, 179 Seedling emergence, by soil rupture, 105 502 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Seedling emergence energy, estimated by penetrometer, 96 Segregation, by sieving, 324 ; by tillage tools, 323 ; method to determine, 322 • of subsoil, 324; tillage objective, 309 Semidigger plow, scouring, 92 Scrapers, filling with soil, 253 Self propelled point, basis for rolling radius, 374; described, 371 Separation, crop from soil, 332 Shape, effect on cutting force, 153; effect on penetration, 185; in design equations, 255; of disks, 242; of soil rolling blades, 250; oriented in path of travel, 269 Shape of plows, empirically described, 228 Shape parameters, plow performance, 225; rolling resistance, 387; tractive performance, 400 Shear, by simple blade, 317; contributions in total draft, 318; contribution in total torque, 273, description by Mohr's circle, 32; effect on compaction, 83; in soil-tool mechanics, 126-133, 141; measurement, 65; measurement in situ, 68; observed in glass-sided box, 36; to assess induced strength, 101 Shear angle, measurement, 135 Shear blocks, on moldboard plow, 169 ; see also soil disturbance and soil block Shear device, misrepresentation, 65 Shear failure, dynamic behavior, 62; effect of soil conditions, 65; in brittle soil, 33; in plastic soil, 33; to describe plastic flow, 39 Shear force, computed from plastic properties, 83-84 Shear measurement, interaction of apparatus, 66 Shear parameters, principle of measurement, 36 Shear plane, see shear surface Shear stress, and soil compaction, 434 ; and tensile stress, 38 ; behavior equation input, 62; compact soil, 72; effect of confinement, 66; equation for vane shear, 70; experimental determination of, 66; maximum, 33-34; measured by squeeze test, 85 Shear surface, angle, 131; change of angle, 136; logarithmic nature, 139; measurement of angle, 135; shape, 134 Shear vane, in situ measurements, 70 Sheargraph, in situ measurements, 69 Shearing cycles, effect on soil weakening, 86 Side angle, effect on disk rotation, 257 ; effect on draft force, 202 ; of blades, 238 Similitude, effect of soil bodies, 194 ; see also dimensional analysis Simulation, by test devices, 64 ; of soil-machine systems, 459 Sinkage, of circular footing, 186; of large plates, 97; predicted by Bernstein equation, 349 ; related to track length, 349 ; soil parameters, 98 Size of cut, effect on blade draft, 254; effect on clod size, 320 338- effect on plow draft, 261, 262; effect on input requirement, 245; path of motion 216 Sleds, towing force, 392 Sliders, to measure sliding friction, 164 Sliding, on plow surfaces, 168 Sliding angle, defined, 170 Sliding distance, effect on draft force of blades, 254 Sliding force, equation, 163 Sliding friction, contribution to draft force, 318; effect of moisture on 49- effect on path of soil deformation, 153; equation, 49; in soil-tool mechanics! 126-133; method of measurement, 49 Sliding path, described, 170 Sliding path length, smearing soil, 164 ; effect on sliding force, 165 INDEX 503

Sliding stress, in adhesionless model, 90 Slip, basis, 369; defined, 346; description, 369; differential on tire, 366, 373; effect on performance, 368 ; effect on sinkage, 380 ; in traction equation, 382 ; of traction device, 345 ; of tractor tires, 370 ; under tires, 362 Slip lines, at incipient soil failure, 136 Small strain theories, limitations of, 18 Smooth tires, power efíiciency of, 402 Soil, a physical system, 55; atomic attraction and properties, 3; cleaning, 332; complex mechanical properties, 3; composite properties, 3; described, 3, 304; dynamic parameters, 60-61; dynamic properties, 14-53; simple behavior, 160 ; simple mechanical properties, 3 ; tensile strength of, 38 ; use of static properties, 57; working or shaping properties, 3 Soil acceleration, by high speed plows, 228 ; measurement during plowing, 485 Soil adhesion, effect on scouring, 178; effect of belt plows, 237; reduced by heat, 236 Soil aeration, decreased by compaction, 430 Soil anchor, equations, 408; for plant residues, 327 Soil behavior, basis for use, 299; effect of soil-tool geometry, 191; in empirical mechanics, 158, in simple systems, 160; in soil-tool mechanics, 126-133, 141; in specific use, 300; in traction performance, 384; on moldboard plow surface, 174 ; relation with physical properties, 306 ; subsystems, 121, 450 ; understanding, 55 Soil bending, in plow mechanics, 176 Soil block, effect of size of cut, 203, 297 ; shape controlled by design, 297 Soil bodies, alteration of tool shape, 192; and edge shape, 244; effect on soil movement, 244; formation and nonscouring, 179; formed by adhesion, 192; hardness, 194 ; on model plowshare, 244 ; on narrow tool, 139 ; on penetrometers, 181; on rough surfaces, 234; on subsoiler, 194; on traction device, 343; types, 129 Soil boundaries, tillage objective, 309 ; see also soil-tool geometry Soil breakup, effect of size of cut, 262 ; measure of performance, 319 Soil characteristics, of wear. 111 Soil characterization, for behavior equations, 57 Soil classification, for construction and trafiicability uses, 421 ; systems, 422 Soil cleaning, from tires, 412; from root crops, 332 Soil cohesion, effect on scouring, 178; see also cohesion Soil compactibility, included in plow mechanics, 175 Soil compaction, agricultural problem, 446; bevahior equation, 431; by blunt tools, 244 ; by kneading action, 440 ; by rotary tiller, 245 ; causes, 431 ; effect on crop production, 430; factors affecting, 431-441 Soil compactness, described, 430 ; effect of compacting force, 432 ; effect on tool wear, 248 Soil conditions, attained by tillage, 298; change with time, 302; changed by climate, 23; changed by forces, 55, 305; changed by tillage, 298; changed by vehicles, 341, 383; changed during manipulation, 101; changed for plant growth, 451; changes described by behaviors, 124; complex descriptions, 303; criteria of performance, 298; description for use, 300; effect of tillage forces, 213; effect on lug effects, 396; effect on power efficiency, 393; effect on scouring, 233; effect on soil reactions, 125; effect on stress- strain relations, 20; effect on subsoiler draft, 232; effect on tillage performance, 213 ; effect on tire performance, 403 ; effect on towing force, 392 ; effect on traction performance, 414; final, 213, 298; fixed for design studies, 215; in plow performance equation, 226; initial, 213, 298; interaction with 504 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE inflation pressure of tires, 413; limitations of direct measurement, 307; measured by cone penetrometer, 424 ; measured for performance, 310 ; modification by new energy sources, 454; persistence of channels, 239; product of past history, 58; role in design equation, 212; role in mobility index, 417 ; role in vehicle performance, 419 ; specific descriptions, 318 ; uniformity for measurements, 311 Soil confinement, by tillage tools, 200 ; use in designs, 297 Soil cores, measurement of strength, 76 Soil covering, typical movements, 241 Soil crusts, measurement of strength, 76 ; method to evaluate strength, 105 Soil cutting, analysis, 184 ; with wire, 317 Soil deformation, by wheel slip, 370; described, 153-155; during cutting, 152, 158; effect of tool geometry on, 153; in glass-sided box, 36; in shear box! 69; path of movement 153; under vehicles, 30 Soil descriptions, based on use, 299 ; for design evaluation, 211 ; simplified by elimination of behaviors, 306 Soil displacement, effect on energy loss, 351; under vehicle, 346 Soil disturbance, effect of chisel angle, 257, 330; evaluated by excavation, 240; residual effects, 239; tool analysis, 292 Soil dynamics, basic research, 124; basic role, 449; classification of variables, 4 ; definition, 1 ; describing subsystems, 450 ; factors affecting, 3 ; history of,' 1-3; key problems, 63; Nichols as a leader, 2; practical role, 458; role in applications, 447 ; role in soil-tool mechanics, 123 ; role in solving problems, 5; role in traction, 456; scope of interest, 299; separate discipline, 450; to define vehicle performance requirements, 456; use in analyzing systems, 458 Soil erosion, increased by compaction, 430 Soil factors, elements of a classification, 4 Soil failure, effect on draft force, 314; see also failure Soil internal geometry, see structure Soil location, methods to determine, 113 Soil manipulation, agricultural importance, 211 ; and transport, 249 ; by tillage tools, 298; controlled by multipowered tools, 265; defined by soil conditions, 298; in U.S., 452; relation with forces, 214; specific tillage objectives, 308 Soil mechanics, use in tillage-tool mechanics, 136-138 Soil mixing, degree of, 326 ; soil renovation, 324 Soil moisture, and plowshare life, 247; conserved by tillage practice 242- effect of barriers, 329; effect on chisel draft, 315; effect on compaction, 440; effect on effective stress, 439; effect on plow draft, 236; effect on sliding force, 165; for plant growth, 303 Soil movement, and wheel slip, 382; around soil body, 244; by bulldozing, 250- by oscillating tools, 282; by plow on slope, 115; 206; by plows, 114- by special blade designs, 253; by tillage tool, 135, 149; by wind, 105; description, 113; effect of tool edge shape, 244; in large scrapers, 253; in relation to vehicle, 348 ; methods to observe, 29, 36, 114, 194 Soil parameters, abrasion, 112; compatibility, 300; dynamic, 60-113, for penetration mechanics, 184; for sliding mechanics, 172; in plow mechanics 147- in tillage equation, 213; in traction equation, 426; independence,' 306i requirement, 455; to assess behavior for plant growth, 303 Soil particles, abrasion characteristics, 53; action in blkst stream, 108-109 and minimum soil deformation, 157; crushed by loading stress. 111; hardness, and wear. 111; method to sort, 112 INDEX 505 Soil path of travel, on moldboard plow, 228 Soil physics, discipline, 451 Soil properties, characterization, 53; effect on -scouring, 233; effect on trafficability, 341 Soil reaction, described by mechanics, 117, 208; effect of blade shape, 251; effect of chisel angle, 257; effect of geometric interactions, 207; effect of lift angle, 238; effect of scouring, 177; effect of soil conditions, "129; effect of tool angle, 331 ; of narrow tools, 139, 205 ; of wide and narrow tines, 204 ; related to tool oscillations, 286 ; separation of active and passive, 57 ; simplified, 57; to evaluate design, 214 Soil resistance, effect of deformation, 154; to deformation, 158 Soil rigidity, as holding body, 297 ; during movement, 39 Soil rolling, blade design for, 250 Soil rupture, method to measure, 262 ; see also rupture Soil sliding path, method to determine, 228 Soil solution, surface tension, 47; wetting angle on metal, 48 Soil strength, and passive behavior, 303 ; and soil-tool geometry, 199 ; bearing, 96; changed by vehicles, 101; definition, 22; described by mechanics, 304; effect on plant material, 330; effect on wear, 112; increased by compaction, 430; induced, 100 Soil structure, calculation from behavior, 306; effect on behavior, 304; effects integrated in behavior, 306; relation with water permeability, 306; role in passive behavior, 304 Soil surface, change during sliding, 161; sinkage, 97, 98, 186, 349 Soil surface profile, method to measure, 116 Soil texture, effect on rupture, 105; in soil classification, 421; material property, 57 Soil tilth, see soil physical conditions Soil truss, for in situ strength measurements, 68 Soil transport, and tillage, 249 ; by large scrapers, 253 ; by tillage tool, 324 Soil use, to determine performance, 298 Soil water stress, effect on shear values, 73-74 ; see also moisture tension Soil wedge, see soil body Soil weight, effect on wear, 112 Soil viscosity, in penetration mechanics, 185 Soil volume, disturbed by tools, 130, 240, see also soil compactness Soil-force systems, classification, 57 Soil-machine dynamics, a discipline, 451 Soil-machine mechanics, to describe physical actions, 56 Soil-machine relations, goal of soil dynamics, 63 Soil-machine systems, as a subsystem, 457; controlled by soil dynamics, 450; factors required, 448 Soil-metal adhesion, method to measure, 46 Soil-metal friction, effect on penetration, 183; effect on scouring, 178; equation for, 161; in soils, 234, methods to measure, 87; principle of measurement, 42 ; see also sliding friction Soil-plant dynamics, a discipline, 451 Soil-tool friction, and design, 233 ; effect of surface conditions, 232 Soil-tool geometry, described, 191 ; effect on cutting, 149, 159 ; effect on forces, 198, 200, 272; effect on scouring, 178; effect on soil movement, 115, 206, importance, 198; of penetrometers, 181; of unsymmetric tools, 201; to exploit soil confinement, 297 506 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Soil-tool mechanics, complete, 122; development, 117; for cutting, 159; principles for development, 118 Soil-vehicle geometry, idealized, 348 Soil-vehicle system, description of performance, 457 Solution filled tires, as ballast, 414 Space link track, performance, 406 Spading plow, performance, 338 Special tillage actions, described, 326 Specific soil resistance, effect of soil deformation, 155 Speed, and effectiveness of oscillations, 286; criterion of traction performance, 368; effect on clod size, 322; effect on cutting angle, 275; effect on draft force, 317; effect on electro-osmosis effectiveness, 266; effect on friction, 40; effect on plow draft, 316; effect on plow performance, 338; effect on rotary tiller torque, 276; effect on sheer, 73, 133; effect on slider draft, 268; effect on soil body, 194; effect on soil movement, 206; effect on tool draft, 263; effect on tool interactions, 289; effect on vehicle performance, 375; in plow mechanics, 176; loading time, 440; locomotion performance, 456; of soil movement on tillage tool, 130 Speed, chisel, effect on clod size, 322 Speed of plowing, effect on stress distribution, 316 Sphere of infiuence, controlled by design, 297 Sprag, equation, 408 Static state properties, changed by active behavior, 57; changed by compaction, 430; changing during actions, 53; described, 53, 55; effect on behavior 304; use, 57 Steel, coeflicient of sliding* friction, 165 Steel wheels, effect on towing force, 387 ; stress distribution on, 357 Stickiness, effect of loading pressure on, 92 ; measurement of, 91 ; not equivalent to adhesion, 91; soil on root crops, 91 Stones, artificial, 455; effect on plow draft, 160 Strain, absorbed in soil mass, 210 ; as a basis for yield conditions, 29 ; definition, 17-20; induced by tools, 238; measurement, 29-^0; observed in glass- sided box, 114 Strain distribution, instrumentation requirements, 31 Strain gages, for tire defiections, 364 ; in the design of transducers, 27, 310-318 Strain gage dynamometer, dynamic measurements, 312 Strain hardening, in soil, 23 Strain measurements, in tension testing, 80 Strain tensor, definition, 17 Strakes, effect on vehicle performance, 411 Stress (es), calculated for soil cutting, 158; calculated for soil deformation 156; controlled in shear device, 70; deviator, 16; effect cycles on compactness, 438 ; measured by track shoe dynamometer, 356 ; on scouring surface, 179; on slip line, 137; on tractive devices, 351; under moving tracked vehicle, 443 Stress concentration, observed in glass-sided box, 28-29 Stress concentration factor, Froehlich's formula, 25 Stress distribution, in granular materials, 23 ; on tools, 314 ; point load theory, 25; to describe soil reactions, 24-25; under circular plates, 25; under flexible wheel. 358; under rigid wheel, 357; under tractive devices, 355- under tractor tires, 26, 361 ' Stress envelope, linear nature in soil, 35; to characterize shear stress 34 Stress indicators, visual, 28-29 INDEX 507 stress in soil, description, 14-17 Stress in tool, effect of soil deformation, 156 Stress sensing diaphragm, location, 27 Stress tensor, application to stresses in soil, 15; effect on compactness, 435; measurement, 436; use in compaction, 431 Stress transducers, diameter-thickness ratios, 28; disturbance of soil, 28; in flexible tires, 358, 361 ; in moldboard plow, 315 ; in track shoe, 356 ; movement during measurement, 27; movement under loading, 362; on chisel, 314; on sliding surfaces, 162, 167; requirements, 362; to determine contact area, 365; to measure distributions on sliding surface, 166; to measure stress distributions, 27, 436, 443 Strength, effect on soil rupture, 103; measured tensile and compressive strength of soil, 37; see also soil strength Stress-strain relations, as behavior equations, 62; as indicators of yield, 32; description, 20; to describe compression, 37; to represent soil behavior, 21-22 Strength of materials, an approach for soils, 22 Structure, relation with behavior equation parameters, 305 Structure failure, orderly fashion, 305 Subsoiler, soil bodies on, 194 Subsoiler draft, measured values, 232; reduced by design, 232 Subsoiler shape, effect on draft, 231 Surface area, effect on friction, 41 Surface curvature, in plow mechanics, 147; description 219-232 Surface roughness, effect on angle of wetting, 49; effect on sliding friction, 234; of soil profile, 116 Surface tension, effect of compounds, 47; effect of temperature on, 47; of materials on glass, 46; of soil solutions, 47; role in adhesion, 42 Systems, development of, 447 Systems analysis, role of soil dynamics, 447

Teeth, on cutting edges, 292; size, number and draft, 295 Temperature, effect on abrasion, 53; effect on adhesion, 48 Tensile failure, at small strains, 80; in plow furrow, 244; measured values for soils, 38; method to study soil factors, 39 Tensile strength, measured in centrafuge, 78 ; methods to measure, 78 ; principle of measurement, 39; principle of method, 74 Tensile stress (es), analysis of, 80; equation for analysis, 75; in a granular model, 38; in Mohr circles, 38 Tetrafluoroethylene, see polytetrafluoroethylene Thrust, description of performance, 457 ; hypothetical force, 367 Tillage, aim, 117; an art, 117; for plant growth, 303, 453; implement, 211; in U.S., 220; objectives, 308, 452; sequence of operations, 454; timed to improve performance, 233 ; tool factors that control, 213 ; without soil inversion, 241 Tillage equation(s), defined, 213; for moldboard plows, 264; principles for development, 217; similarity with traction equation, 383 Tillage forces, based on reasons, 308; defined, 211; energy expended in, 220; immediate effects, 302; sequences, 454 Tillage performance, of different plows, 338; past objectives, 452 Tillage speed, effect on clod size, 322 Tillage tool(s), defined, 117, 211; effect on clod segregation, 323; efficiency of soil breakup, 104; interactions, 289; technique for design, 215; to loosen and turn soil, 220; wear. 111 508 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Tillage tool design, empirical, 211; governs use, 454 Tillage tool mechanics, empirical development, 218 Tillage tool movement, role in design equation, 212 Tillage tool shape, role in design equation, 212 Time dependence, viscoelastic soil in penetration, 185 Tine arrangement, guide for rotary tiller, 279 Tine construction, effect on performance, 400, 402 Tine design, to reduce drag, 278 Tine parameters, effect on work input required, 274 Tine shape, for rotary tillers, 271 Tine size, sphere of influence, 203 Tire carcass parameters, effect on performance, 400 Tire chains, effect on vehicle performance, 411 Tire deflections, measured, 370; methods to measure, 363 Tire descriptions, conventional and radial-ply, 402 Tire design factors, interactions, 395 Tire loads, increased by hitching, 415 Tire lugs, effect on power efliciency, 403 Tire parameters, described, 404 Tire performance, power efliciency as a criterion, 374 Tire size, effect on performance, 414 Tire tread, effect on traction, 398 Tires, solution filled, 414 Tool(s), interactions, 207; sphere of influence, 203 Tool angle, changing on rotary tillers, 275 ; effect of oscillation, 286 ; effect on chisel forces, 257; effect on penetration, 259; effect on soil reaction, 331; effect on soil-tool geometry, 292 Tool depth, travel distance to penetrate, 259 Tool descriptions, for design, 216 ; principles for development, 219 Tool design, based on soil reactions, 296 ; consistent with use, 231 ; equations needed, 265; for specific soil handling, 253; principles for study, 215; to cover surface material, 242; to increase soil disturbance, 240; to segregate soil, 324 Tool edge, effect on soil compactness, 244 ; see also shape and wear Tool efliciency, effect on tool shape, 263; performance, 298 Tool forces, dependent on soil conditions, 213 ; effect of edge shape, 243 ; effect of soil-tool geometry, 272; effect of wear, 246; method to measure, 312 Tool friction, reduced by air blast, 236; reduced by plastics, 235 Tool geometry, effect of wear, 194; inclusion in mechanics, 154; length : width ratio, 203; penetrometers—shape and resistance, 182 Tool macroshape, described, 221; empirical development, 238; qualitatively described, 230 Tool material, and tool wear, 249 Tool mechanics, objective, 117 Tool microshape, and soil body formation, 234; described, 232; effect on performance, 233 Tool movement, coordinates for description, 260; described, 255; equations for oscillating tool, 284; of rotary tools, 275; required for penetration, 259 Tool operation, consistent with use, 231 Tool orientation, complex nature, 256; effect on forces, 201; effect on performance, 257 Tool oscillations, effect on cutting force, 280; relation to soil failure 288- spontaneous, 279 ' ' INDEX 509 Tool parameters, effect on cutting force, 190; effect on draft of chisel, 315; effect on oscillated tool draft, 284; effect on wear, 112; fixed for design studies, 215 ; for cutting teeth, 293 ; in plow draft equations, 264 ; in tillage equation, 213; penetrometers, 184; relation with torque, 274; rotary tiller tines, 273 Tool path, rotating tool, 275 Tool penetration, increased by suction, 259 Tool performance, calculated by mechanics, 121; governed by judgment, 308 Tool shape, and soil-tool geometry, 261; design factor, 219; functional concepts, 253; mathematical description, 219 Tool sharpness, effect on cutting resistance, 248 Tool spacing, effect on cleaning, 277; effect on geometry of cut, 278 Tool suction, effect on depth control, 259 Tool symmetry, effect on forces, 201 Tool wear, accelerated in wheel track, 248 Torque, effect of tine arrangement, 277 ; effect on tine spacing, 278 ; of rotary tiller tines, 272; of rotating plows, 338; optimized by design, 276; requirement for traction, 382; tire input, 367 Torsion shear, equation of stresses, 68 Towed point, basis for rolling radius, 374 ; of wheel, 371 Towing force, effect of weight, 386; equation for, 390; of sleds, 425; of tracked vehicles, 391, of trailers, 392; of wheeled vehicles, 425; predicted by rating cone index, 425; reduced by pneumatic wheels, 387 Tracers, to determine soil movement, 113; to measure soil mixing, 115; to study mixing, 325 Tracks, design, 405; flexible design, 410; towing force, 392 Tracks (half tracks), effect on vehicle performance, 411 Track width, effect on pull, 408 Traction, defined, 1, 340 ; effect on soil condition, 383 ; grip and ground failure, 348; work done on soil, 353 Traction design factors, identified by measurement, 384; operational control of, 413 Traction device(s), characterization, 355; design, 381; dynamic stress distribution imder, 355; forces on, 409; power efficiency low on soil, 340 Traction efficiency, ideal, 351 Traction equation(s), described, 382; for lugs, 408; method of development, 383; similarity with tillage equation, 383 Traction force, determined analytically, 350 Traction in U.S., annual cost, 340 Traction measurement, NIAE apparatus, 9; NTML apparatus, 378 Traction mechanics, described, 385 Traction performance, empirical equation, 384; evaluation by comparison methods, 384; improved by traction aids, 411; of powered wheels, 393; of radial-ply tires, 402; prediction of, 420 Tractor tires, stress distribution on, 361 TraflScability, defined, 341; related to soil conditions, 57 Trailers, towing force, 392 Transmission activities, a basis for soil use, 301; in soil behavior, 55 Transmitted force system, in passive behavior, 55; in tillage evaluation, 303 Transport devices, characterization, 355; design, 381, 386; nonrolling, 342; rolling, 354 Transport performance, evaluated, 388 510 AGRICULTURE HANDBOOK 316, U.S. DEPT. OF AGRICULTURE Triaxial shear, in measuring compaction behavior, 83; modified for volume strain measurements, 70

~~Ultimate stress, in compression, 36; in tension, 37 Use, basis for evaluation, 366~~

Vector analysis, to define force resultants, 313 Vehicle(s), and traction, 340; effect of slope of terrain, 206; effect on soil strength, 102, 424 ; weakening of soil by, 86 Vehicle action, simulation by plate penetrometer, 100 Vehicle capabilities, role of design, 417 Vehicle cone index, described, 424 Vehicle design, for different soil conditions, 341 ; interactions, 416 Vehicle morphology, effect on performance, 416 Vehicle parameters, in traction equation, 426; in traction mechanics, 342 Vehicle performance, predicted by dimensionless terms, 426; predicted in sand, 427 Vehicle stability, on slopes, 418 Vehicle traflicability of soil, prediction system, 423 Velocity, see speed Vertical tool, mechanics, 139-148 Vibrations, of track vehicle tracks, 356; see also oscillations Viscoelasticity, applied to stress-strain relations, 21 Viscosity, effect on adhesion, 49; in plow draft equation, 264; in traction equation, 426 Volume strain, in compaction, 437, measurement, 30 Volumeters, to measure air displacement, 30; to measure soil compaction, 435 AVater, see moisture Water conservation, decreased by soil compaction, 430 Water movement, effect on adhesion, 91; by electro-osmosis, 266; effect of wheel slip, 445; energy required in electro-osmosis, 266 Wear, accelerated in wheel tracks, 248; alteration of forces by, 196; and tool stability, 197 ; assessment, 197 ; effect on depth of plowing, 247 ; effect on soil condition, 245; effect on tool geometry, 194; factors affecting, 112- laboratory-field correlations, 111; methods to assess, 110; of disks in ganes' 249 ; of metals, 53 ; rate, 246 Weight, compensation by differential lock, 418; effect on coefficient of traction, 379; effect on towing force, 386; effect on friction, 51; effect on tire deformation, 371; effect on traction performance, 382; to improve performance, 413 Weight transfer, to tractive device, 379 Wettability, and soil adhesion, 47; angle of wetting, 48; effect on sliding actions, 167 Wheel, effect on tool wear, 248 ; towing force, 392 Wheel diameter, effect on rolling resistance, 388 Wheel performance, effect of lugs, 394 Wheel shape, effect on towing force, 390 Wheel size, effect on rolling resistance, 389 Wheel slip, effect on water infiltration, 445 Wheel width, effect on rolling resistance, 388 Width of cut, effect on plow draft, 262 Winch sprag, design, 409 INDEX 511 Wind, effect on soil movement, 105 Wings, to increase soil disturbance, 240 Wire, installed in soil, 330; to clean mud from tires, 412; to cut soil, 317; to handle plant residue when plowing, 327 Work, by tools on soil, 104; done to soil, 263, 337, 353; effect of cutting angle, 276, effect of teeth on, 294; measure of vehicle performance, 380; performed by tractive device, 375; required for tiller tines, 274; to break up soil, 274; to cause shear, 72 Work hardening, compaction hardening of soil, 23, 100; see also strain hardening

~~Yield, as a terminal soil behavior, 31; definition, 32 Yield criterion, a subjective quantity, 32~~

~~Zero normal stress, in cohesion model, 38 Zero slip, location of, 371 ; methods to describe, 372~~

~~U. S. GOVERNMENT PRINTING OFFICE : 1967 O - 222-179~~

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